Using the terms Vacation Rentals Fairplay and entering 7 guests, and cabins as the type of property.
A quick search near Fairplay for Christmas week, Dec 20 - Dec 27, found a lot available from $250 per night on up.
The town of Fairplay has a lot of wooded sites in the listings.
If Fairplay does not work for you, use VRBO search and use their Map function to find places you like.
I have been using VRBO since they started decades ago and have managed to find affordable places all over the country when I get a week to 2 months free for fun.