If you study weather maps of the US as much as I do you'll quickly realize that the Western half of the US is in general much drier than the eastern half. With the exception of the Pacific coast and some higher inland terrain most of the western US can be considered semi-arid and is made up of vast deserts, arid scrub and steppe grasslands and savannas. This is mainly because the mountainous terrain creates rain shadows from weather systems that come in from the Pacific ocean. Western Washington and Oregon are quite wet most of the year, but the huge Cascade and Sierra Nevada ranges block most of the moisture off the ocean from reaching the barren interior. This makes growing food plots in most of the west very difficult, especially when compared to the rain soaked eastern half of the US. However, even though it is more difficult there are some general guidelines that can help those living in these areas create great forage opportunities for the wild game on their property.
For as dry as the western US is, in most areas you will have at least a portion of the year with enough precipitation to establish a food plot. Most of the west has a rainy and a dry season, which can help you determine the best time to establish your plot. These seasons differ however, based on where exactly in the west you are located. As a general rule the northwestern US from extreme western Montana all the way to the coast and down through southern California as well as most of the higher terrain throughout the west will have a winter peak in precipitation. Most of this falls as heavy snows in the mountains and foothills, but in the lower elevation areas such as the Columbia Plateau most of the precipitation will fall as rain.
East of the continental divide from Montana and Wyoming and east to the great plains will have a peak of precipitation in spring and early summer. These areas will generally see large spring thunderstorms move through as moisture from melting snow in the mountains is blown east and causes instability in the atmosphere.
As you go south into central Colorado, New Mexico, Arizona and southern Utah you start to get summer monsoonal moisture that comes up from the gulf of mexico and tropical pacific. These are also usually large thunderstorms which can sometimes produce torrential rainfall in areas that are usually thought of as deserts.
Then from western Colorado into most of Utah you usually will get a small peak of precipitation in the fall. In the areas of true desert from Western Utah, Southern Idaho, Eastern Oregon and most of Nevada and parts of California and Arizona you may not be able to grow much of a food plot because these areas have very low precipitation spread out through each month. But other than those areas of true deserts most of the west will have at least a month or 2 of moderate average precipitation where a food plot could potentially be established.
Another way to determine what will do well in your area is to look at what kind of herbaceous plants are already in your area. Are they warm season grasses? Cool season winter annual weeds? Whatever the dominant vegetation is will really help to narrow down the types of plants that would do well in your area.
Once you've figured out the wettest time of year for your region and observed and researched the natural vegetation in your area it's time to look at what types of plants will actually grow in your specific climate. For areas of the Northwest mixes made of late fall planted winter annuals do very well because they are hardy enough to survive the cold of winter as well as take advantage of winter precipitation. Cereal grains like Winter wheat and Winter rye are some of the top choices for this area and are actually grown as crops in many areas of the northwest. Other potential plants that would do well are annual clovers such as crimson and balansa as well as hairy and common vetch. Winter Camelina, a unique brassica, is also a good choice for this region because of its great cold tolerance.
For the Northern plains and northeastern Rockies you'll mostly want to focus on spring annuals such as spring wheat and spring peas. Also in most areas some more cool weather tolerant summer annuals could be used such as sunflowers, buckwheat and safflower. Another good option for this area is Alfalfa because of its drought hardiness and mainly spring focused growth.
For the monsoonal climates of the southwest, summer annuals such as those previously mentioned as well as more heat tolerant types such as lablab, cowpeas and grain sorghum could be good choices to take advantage of the heat and summer rains. I also think late summer planted fall mixes would probably do well here such as brassicas and even some of the more cool season species such as annual clovers, vetches and some winter cereal grains.
And then for the areas with a fall peak in precipitation the summer annual buckwheat would probably do well because of it's fast growing ability that could take advantage of the last bit of warmth before the first fall frosts. And then most of the fall-planted winter annuals that do well in the northwest should also do well here.
For areas of true deserts and low rainfall all year it will be very difficult to create a mix that does well, however there are some exceptionally hardy plant species that might be able to take hold with just a small amount of moisture. One very drought hardy option would be small burnet. This plant can grow in areas with annual precipitation in the low teens and its seed is able to sit in the soil for long periods of time until a passing shower produces just enough rain to germinate it. I've planted this species on some of the more harsher south facing slopes on my property and it has thrived where other species have struggled along at best. Some other potential options for really dry areas are winterfat and forage kochia. These are both actually subshrubs and are exceptionally hardy to drought and would probably do well across most of the west, especially in areas that are too dry for other common food plot species.
Another important thing to keep in mind is that because of the sometimes unpredictable climate you may not get the seasonal rains for your area at all. Droughts can be very common in the west and sometimes this might cause your food plots to completely fail. However, I believe that if you take care of the soil on your property by practicing regenerative style management and by using permaculture techniques then this will add resilience to your ecosystem and you'll be able to grow more than you otherwise would if using more conventional food plotting methods. That's why in the west it is especially important to use those methods that help build soil and retain moisture on your property, such as no-till and diverse mixes, and will help you grow high quality forage for wild game under relatively difficult and unpredictable conditions.