We recently had a local private indoor tennis facility go bankrupt -- much to our collective chagrin. The place had had six courts, went to five, then, four, and later three over its 30-year lifespan (western Wisconsin). Each successive court was replaced by the flavor of the day -- racquetball, a pool, nautilus/aerobics equipment, etc. Simply put, the owner tried to compete with non-tennis venues and failed, despite the courts staying reasonably busy.
Our winters are much worse than yours sound, though, and indoor tennis is the only alternative from November - March. Many of the locals now commute 30 miles to an indoor club across the river in Minnesota to play. Some drive further for leagues.
There's a lot to consider: who will build and pay? Where's the revenue -- in memberships, fees, leagues/lessons/events? Is there a pro to manage and draw people to the courts? Would any schools or teams provide any income?
Given that tennis courts are costly and require substantial square footage per participant, I'd think a new indoor facility a shaky proposition, especially when it would be used intensely just a few months of the years, as yours might. Almost no one plays indoors here from May-September, by the way, unless the rain is torrential.
I say all of this hoping, though, that we get a new facility here in the future.... For it to happen, it takes some capital, a vision, some passion for tennis, and a real plan.