I use a wooden TV tray as well and it gets used heavily when I'm piecing. I've yet to damage the tray and I've got an iron that can bring the heat and steam when I want it. A couple of suggestions, though...
One, tell your friend if she's worried about the wood underneath, she can lift her wool mat at the end of the night and let it dry out completely. That way, the wood isn't subjected to a lot of hot moisture for any longer than it needs and the wool has a chance to air and dry out.
Two, I just recently moved to a mini travel iron because I was having some issues moving things around with my big iron, it still gives steam and still brings the heat, but I've noticed that my mat isn't that heavy at night like it was with my big iron. I also noticed that it doesn't take long for the mat to air out completely. Maybe switch to a mini travel iron if it's possible and save the regular iron for pressing quilt tops and yardage.