Nancy Lake Recreation area is pretty close, safe and an easy ride. Hatcher's Pass is fun but currently probably a bit dangerous. With all the recent snow loading, avalanche danger is a distinct possibility for someone who doesn't know the signs.
For Nancy Lake, just take the Parks highway North through Wasilla, past Houston and turn left on the big, wide, plowed road to the Nancy Lake Recreation Area. The road will end in a few miles and there is parking on the left side. You'll have to pay to park. Unload there and continue by snowmachine down the road until you can drop down onto North Rolly Lake and follow the fairly well travelled trail to Redshirt Lake. There, be careful for overflow, but you can follow where ice fishermen and others who know the area well have gone and you should be fine. Along the way, there's some smaller lakes and ponds you can drop down onto and play around too!
Go to Yahoo! Maps, type in Wasilla, AK., zoom in a bit and pan the map past Houston till you see the Houston Cutoff and you'll see what I'm talking about.
My wife likes that little ride. Tomorrow, we are heading farther north past Trapper Creek to my buddie's cabin for an overnight stay. I can't find any reliable condition reports for the area North of Petersville, so I guess we'll go find out for ourselves. We are taking our little 4 yr old all bundled up, so if it's close to zero or sub-zero, we'll have to turn around. I don't want to risk her getting frostbitten. If we ride, I'll share the snow report when we get back.
Have fun, and be safe. Happy New Year everyone!