Powderville is a great area, the hotels are in Broadus. I hunt antelope out there quite a bit and do see some good mule deer. There is a LOT of public land around there (look east, on the road to Ekalaka, you'll cross lots of BLM) but you need to know where you are (compas, GPS) to stay on public land.
Do yourself a huge favor and buy the Powderville, Broadus, Alzada and Ekalaka BLM 1:100,000 maps and study them before you go. Look for areas where there's good cover (terrain, trees, etc.), where the ATVs can't get, park your vehicle and walk a mile or so in.
You many also want to get the Block Management guide for Region 7, 406-234-0930 and look for walk in only areas. Beware, lots of block management areas have poor hunting.
Blue Tongue disease (whatever the real name is...) hit the whitetails hard a few years ago, but there are plenty. As stated above, watch the weather! I was shooting prairie dogs east of Powderville a few years back and almost lost it in a torrential downpoor/tornado, and all I got was one lousy prairie dog.