So far the ones I've seen look pretty decorative and don't appear to look sturdy enough to handle the wet environment, but I have not seen one in person. Anyone know what sort of BTU they claim?

for a greenhouse you are better off with a "blue flame" or "space heater" These kinds of heaters are used to heat the air. An infrared heater is used to heat objects directly...it's why when you're in front of one it feels nice and warm.