Alright...well, basically a winter ascent up the Lions Head is often not that big of a deal ON A NICE DAY...this is key. Seriously, try to choose a day with a good forecast...especially keep the wind in mind. In terms of gear you will need some kind of mountaineering boots, crampons and an ice axe...all this you can rent at the three North Conway equipment stores IME, EMS and Ragged Mountain (I think this website has links to them). Also key is enough clothes...even if the forecast is good, it can get cold and nasty REALLY fast. Lets see what else...have a map with you and look at it beforehand to get an idea of where things are...sort of a visual picture of the terrain before you head out.
Don't forget to take the WINTER version of the Lions Head trail. It goes off to the left soon after the second bridge off the Tuckerman Ravine Trail onto a tractor road, but then very quickly turns right. There are sings - just don't miss em!
The steep section begins soon after this interesection and ends around treeline. It's pretty steep, but shouldn't be too much of a problem for people in good shape.
Above treeline make sure you follow the cairns and stay on the trail. Usually you will know where the trail is as it will be relatively packed out, but not neccesarily.
The descent of the steep section might take more time than the ascent, but again if you're generally athletic it shouldn't be a problem.
good luck dude