Over 10yrs ago I was tired of getting cold on the frostiest of days after hearing all the stories of my buds using propane heaters and staying warm so I bought a BIG double burner heater and hoofed a 20# tank out to my prize shooting house. I remember one particular incident during muzzleloader season where the afternoon was warm enough that I didn't carry a jacket with me. Well as the sun dropped and the woods started quickly cooling during the last hour of light I was getting cold. I kept looking at that heater over in the corner of the blind until finally I thought, "Why not?" so I fired it up. The wind was blowing out in front of the stand (didn't matter as most of the deer traveled out the left side of the stand 100-200yds away) and a mature doe came down the field edge, slowing feeding towards me. Now these deer were consistently pressured and they ALWAYS jumped out of their skin, did a double back flip and took off blowing across the countryside alerting everything when they so much as got a single molecule of human scent in their snooter!

So I knew it would be a "quick and fair test".
Well here she came, as she got about 10yds away from my "wind/scent stream" I thought, "Well this will tell the tale". Sure enough she got to where she could smell me but she didn't hightail it. She DID "kinda sorta" go on alert, she forgot about feeding and started "investigating" this scent. She walked circles, sniffed up and down, looked and looked and looked. But in about 2-3mins she went back to feeding and continued on down the field edge. I knew then that the propane was hiding/confusing enough of my scent from her that it would be ok. I also surmised that in that rural area of west TN where I was hunting, that EVERY house/trailer/shack out there was on propane heat so it's got to be a natural part of their environment as a result. I think the doe was just "curious and perhaps a little confused" as to why all of the sudden that scent was in that field where it had never existed before, but as I said it didn't bother her enough to react negatively and make her leave.
Honestly I was more concerned about the noise the pilot light/ignition system makes while burning but I've had deer at bowrange never seem to hear it, if so they've never alerted on it. You just have to be careful with the heaters in the confines of a small shooting house/blind as they can not only ignite flammable materials but more likely they can melt/ruin things like your boots, heavy outer clothing, wool, chairs, nylon sling on your rifle etc before you realize it. Just be mindful and MAKE SURE they are cooled down properly before you store them or leave the blind!