I'm thinking of setting up a drain from my sauna through the floor of my house into my crawlspace. Practically speaking, would this damage the house?
Yes, it could lead to wood rot and a severe mold problem. Don't do it.
Put the drain down through the floor like you were planning. Add a j-trap (like under your kitchen sink).Add more pvc to reach the floor of the crawl space. Add a 90 degree turn,then add horizontal pvc to the outside of your house. When you come to the outside stop. Dig a trench about 6 inches or less (enough to cover the 1 1/2 or 2"pvc). Make sure it goes far enough from the house so it won't drain back through the ground into you basement (or back under you house into the crawl space usally 6-7 feet). Where the pvc stopped at the outside of your house add a 45 degree coupling,then a short piece of pcv (2"), then another 45 degree coupling then enough pvc to the end of your trench. Cover the pvc. Leave the end open(or put an unglued cap on the end to keep rodents out). now when you want to drain the sauna go out take the plug out, pull the plug on the sauna and drain. After draining, put the plug back in. It doesn't take long for the sauna to drain.You really don't have to cuver the pvc outside the house, but if you do you can mow over it without having to move it all the time. This is exactly how I did the baptistry drain for our church when we were finally able to purchase and install our baptistry. If you were to simply drain the water into your crawl space eventually there would be so much mold you woud have to abandon your house.