While there is no hot tub directly at Mountain Lodge, Snowshoe's Split Rock Pools are located immediately across the parking lot from the building. In my opinion this is much better than most of the hot tubs located in other buildings around the mountain.
Enjoy indoor/outdoor hot tubs and pools, waterslides, a sauna and locker rooms. Make sure to bring your bathing suits -- towels are provided. The pools are open Open Seasonally, Summer and Winter. The operating hours vary, so call 304-572-5680 before heading over.
Split Rock Pools has a charge of $7 per person -- it's free for ages 3 and under.