I'm looking for a cozy Inn in February. Not too expensive, that has quaint shopping for the ladies and skiing for the men. It is okay to drive to skiing a short while. We just have never been to NE and want to be able to snuggle by a fire or go ice skating and local shops.

Salt,
There are many options, and you should get many suggestions.
I offer the Mount Washington and Mad River Valleys.
The Eagle Mountain House and The Christmas Farm Inn come to mind...
http://www.selectregistry.com/locateinn.aspx
Alternatively, the Waitsfield Inn in Waitsfield, VT
http://www.waitsfieldinn.com/

NH is heavy on shopping, VT is heavy on relaxing.

More information is needed: where are you coming from? Are you flying or driving? What week in February (you may not be able to get reservations now for school vacation week)?

Here are some nice places in central Vt:

The Quechee Inn at Marshland Farm - beautiful place just outside the town of Woodstock. On premises x-c skiing.

The Round Barn Inn at Waitsfield - Another beautiful place just a short hop to Sugarbush ski area.

I'll top this thread with a vote for Vermont. Sorry, no specific suggestions for an inn, but I used to live there and it is one GORGEOUS state.

we spent Christmas with family and stayed at the Kedron Valley Inn, in South Woodstock, Vermont. though we didn't ski, some big places (like Killington) are nearby, some small places (Suicide Six) are even closer. there is cross country skiing down the road on the golf course of the Woodstock Inn. Ice skating on the ponds if cold enough or at the indoor rink in Woodstock. you'll find good shopping and good eating in the village of Woodstock. the Kedron Valley Inn has three buildings. the main one is where we had breakfast each morning (a full breakfast was included in our room rate). it's good and filling and served in the dining room: very New England farmhouse with beamed ceilings, fireplaces, and views of snowy woods out the windows. we stayed in the newer one story motel type unit which is done up in rustic log cabin in the Adirondacks style: working fireplaces are a plus. our rooms had private baths and TV's but no phones.