Hi, I have this lift kit installed: PRO-TRUCK LIFT SYSTEM (Stage 1) - TOYOTA 4Runner Base

And my OEM tires are due for replacement. I'm having a kid in february and I have an hour drive on country roads to get to the hospital, so I am thinking it might be a good idea to get fresh rubber on there just in case the weather is bad that day. Preferably something that also does well for off-roading. The OEM tires are mall-crawlers and while they do great on-road, they are completely worthless off-road.

The truck is basically a spare vehicle so treadwear rating is irrelevant and so is on-road ride quality (as long as it's not complete torture). I live out in the country and I have trails out on my property so I would like to get something with more off-road focus.

What size / model tires would you guys suggest for going up in size (but safely within the contraints of my lift) and have better mud / snow capability?