Is 10/3 @ 240 with ground good enough for a short run from sub panel to sauna heater?
Assuming you are in the US and subject to NEC, 10 gauge copper is strictly limited to 30A. So, no.
I don't think 8 gauge is big enough, either, unless it's THWN in conduit and the connections at both ends are rated for 75C. The breaker protects the wire, so you can't play games with sizing the wire for 37.5A. Given it's a heater, you need to provision for 125% of the load as a continuous load, which is 46.875 amps, which gets to why you have a 50A breaker, not a 40A breaker.
If using cable, which is limited to 60C sizing, you need 6 gauge copper or 4AWG aluminum. Which begs the question of what size breaker you have on the 4/3 aluminum you ran out there, since that's limited to 55A if it's 4/3 cable.