Eastern Oregon is very sparsely inhabited, especially in the southeast counties. Always make sure your vehicle is in good working order and that you carry extra fuel and food. Help can sometimes be a long way away and cell-phone services is spotty.
The high-desert environment is one of extremes: autumn and winter can bring harsh snowfalls, while daytime summer temperatures can easily reach ninety degrees or more with considerable drops at night. Of course, altitude variances compound the issue: it could be 80F and sunny June day in Burns 4147' / 1264 m yet snowing on Steens Mountain 9733' / 2967 m - a major regional attraction - some seventy miles away. Always check the weather conditions of where you are and where you are going frequently, and carry layers of clothing so that you can adapt to any sudden changes.
Yes, there are rattlesnakes. No, they won't hurt you if you don't bother them. Same goes with the rest of the wildlife, to which the same usual rules apply: don't feed them, don't approach them...just leave them alone.
Be aware of hunting season if you plan on tromping around by foot and dress accordingly.