It's been decades since I lived there, but Vermont has few restrictions, period. http://www.handgunlaw.us/states/vermont.pdf
There is no restriction specific to biking. Given how much more liberal VT has become, it's hard to believe Constitutional carry survives there, but survive it does. You're bound to get some dirty looks from the crunchies.
I don't know what policy the Trapp Family Lodge might have on its private property. It may have changed over the years, but their Black Forest cherry cak e and Viennese cinnamon coffee used to be amazing.