I lived the first 24 years of my life in NH and miss it every day. Where do I live now? Hawaii.
The COL in NH isn't excellent for mustachians, but it does have a lot going for it. Others have mentioned no sales tax and no state income tax. Very helpful for younger mustachians, but not as advantageous for someone who's looking to buy a home, since most of the state's revenues come from property taxes. When looking for a home and a job, obviously look for a short commute. NH has several toll booths, so also be aware if any are between your work, your home, and where you like to spend your time. If you live in Merrimack but work in Nashua and like to ski up north, you'll hit a toll booth almost every day (twice!). I grew up in Manchester, and we hit the tolls south of Concord when we went skiing, and the tolls on the way to Nashua a few times a year. There's another set in Portsmouth, but I think I've driven through those fewer than 5 times in my life- those are positioned more to take advantage of Massachusetts drivers coming up into NH and Maine. ;-)
The falls are beautiful and there's tons of place to hike, kayak, bike, run, etc. There are hiking clubs that climb the 4,000+ footers and part of the Appalachian Trail goes through NH.
Winters are obviously a little harsh, but very pretty in their own way. Ice storms are extremely dangerous, but those days are some of the prettiest I've ever seen: no one outside, moonlight glittering through the ice on the bare tree branches, smooth snow as far as the eye can see because everyone is inside. I miss it. If you buy a condo, you'll have higher fees but the condo association typically takes care of snow removal of the driveways and sidewalks (though you're usually responsible for your own front walk and front steps/porch, so don't sell your shovel!). And you can ice skate on lakes and ponds- I'm amazed at how many people I've met who have never skated outside an ice rink. And NH has a lot of ski areas if you ski or snowboard (very unmustachian, but part of the fibre of my being).
Springs are awesome, partly because you appreciate them so much more after the winter. I miss the smell of fresh earth and the bright green buds on the trees, and there's a distinct earthy smell about a spring rain you don't get the rest of the year.
And summer is more comfortable than places to the south, but stock up on bug spray because the mosquitoes come out in force around sunset each night. NH has a whopping 13 miles of coastline and the ocean is pretty cold even in summer, but the lakes get comfortable.
NH is the place for me, and I look forward to moving back there some day. :-)