Good luck on your hunt!! I lived in Green River (Sweetwater County) Wy for 17 years - never thought I'd leave, but...still chasing the dollar and had to leave for work. Your short answer is NO - you only NEED a guide if you are hunting in the Wilderness Areas. These are plainly marked on the maps as a Wilderness Area as oppossed to a National Forest, a State Forest, or whatever. There are literally tons of roads in the Rawlins areas. There are huge gasfields at nearby Wamsutter and the place is littered with roads. You will find some private lands, but they are usually well marked. The public lands are huge and very accessible. You should find VERY good quantities of both deer and antelope all over. We travelled through to the Denver area every month or so and were never disappointed in seeing game. Don't recall any Wilderness Area anywhere near Rawlins, so you should be fine. If you have a GPS, take it and use it. The country is big and it all looks alike. If you don't have one, you might consider getting one and learning how to use it before you go. I bought a GPS for my work when I came to North Idaho, and I couldn't hunt here without one - it's so thick and you can't see anywhere to get oriented. Hope this helps.
Regards,
Sweetwater