Enjoyed some great late March skiing in that neck of the woods at Wildcat in 2005: http://www.dcski.com/articles/view_article.php?article_id=838&mode=search
Have not skied Loon, but have driven by and know it is a sizeable place close to WV and Cannon. Have skied the later two, preferred Cannon, but WV good too. Late March can be dicey even that far north and I wouldn't buy lift tickets far in advance. Could be reduced number of trails open, but chances are some decent skiing will be found within 1 hour drive from Lincoln. Wildcat and Bretton Woods have reputations for remaining open into April in recent years, not sure about the others. I'm not that familiar with Lincoln, IIRC it has cluster of motels, restaurants, but not much else. A visit to Bretton Woods, even if not to ski, might be interesting because of historic hotel complex. I stayed in North Conway when I was up there in 2005. It has more of an established town with restaurants, businesses, and lots of outlet shops (which is a positive for some and a negative for others).
I like NH, it seems less touristy and developed than VT, notwithstanding North Conway. Nothing quite like Mt Washington in VT. But I'm sure Stowe, VT would be a good candidate for your plans too though.
Does your timeshare cover Quebec City? Now that's a destination for a mixed group of skiers and nonskiers looking for late spring skiing in the East: http://www.dcski.com/articles/view_article.php?article_id=1145&mode=headlines