I just do both. While there's less of a risk on the back tire since I'm already doing the front I seen no reason to increase risk by not doing the back.
For tires I'd suggest the 45nrth Xerxes:
45NRTH | Unparalleled Cold Weather Performance
At high pressure the studs don't come into contact with the ground unless turning or slipping. At least pressure they do contact the ground. You can adjust by changing tire pressure without going through the hassle of removing the tire / rims / etc.