the main concern between cheyenne to utah is wind. i 80 closes with any major storm because of the drifting snow across the HWY. Another thing to consider is the amount of semi-trucks on 80. None of them can drive period, so forget about it in the Winter.
I haven't made the drive past cheyenne, but I know that on the Utah side there are always the automated signs with road conditions: "Chain required" or "i 80 westbound closed at mile marker__".
Chains or 4wd are required. Just be smart, and you should be straight, you'll know before you leave cheyenne if you're going to need to stop into town to wait the storm out.