Why are my helmet visor prints coming out cloudy after sanding?

The frosty look after drying is just what sanded resin looks like, so no, you didn't do anything wrong. Sanding leaves microscopic scratches that scatter light, and they only disappear when something fills them in. Water fills them while wet, which is why it looked good mid-sanding. The heat gun trick kind of works because you're briefly melting the surface, but on a big curved visor you'll never get it even before you start warping things, so I'd drop that idea. The actual trick people use is to polish instead of stopping at sanding. Go through your wet sanding grits as high as you can, then follow with a plastic polish compound on a soft cloth or a buffing wheel on a low-speed drill. That's what acutally removes the fine scratches rather than just making smaller ones. If you stop at sanding and spray clear coat over it, the coat will fill the scratches and look glossy, but you'll see every sanding mark frozen under the gloss. It looks okay from a couple feet away, less okay up close. The two-part epoxy is what people use when they want that glass look with less elbow grease. You mix a small batch, brush or pour a thin layer on, and it self-levels and cures hard like glass. The drip problem is real, so the usual approach is to do it in stages: tilt the visor so it sits flat or near flat, apply a thin coat, and let it kick off before moving it. Some people do one face at a time. Mask off the edges and any holes first so the drips have somewhere harmless to go. Don't try to brush it thick, thin coats self-level much better.

If you polish first and then epoxy, you can get away with a slightly less perfect polish because the epoxy fills what's left.

On the FDM side, yes, PETG visors come out cloudy too, mostly from layer lines and moisture in the filament, but people fix it the same way, sanding and polishing or a clear coat. Resin will get you closer to clear with less work, so I'd stick with what you've got rather than redoing the helmet.

I'd push back on the epoxy part. On anything with curve to it that stuff is a nightmare, it runs to the low spots no matter how thin you brush it and you end up sanding the pools back down anyway. I did a faceplate a while back, went to like 2000 grit wet, hit it with a couple light coats of spray clear and it looked fine. Sure, up close you can spot it if you're hunting for flaws, but nobody's inspecting a helmet at a party. For a costume that only has to survive one night, the epoxy route feels like a lot of mess and cure time for a difference maybe two people will notice.

Second guy has it right about the epoxy on curves, I fought that battle once and never again. What worked for me was a cheap buffing wheel on a cordless drill at low speed with the finest polish compound, after wet sanding up through 2000. Took maybe 20 minutes on a visor about the size of yours. Only thing I'd add is keep the drill slow, resin heats up fast on a wheel and you'll get the same warp problem you saw with the heat gun. The polish alone got it clear enought that I skipped any coating entirely.

Quick update — the buffing wheel suggestion worked perfectly. I followed the advice to run it over the visor with a fine polish compound after getting it all wet sanded up to 2000 grit. It fixed the frosty finish and it looks completely clear now!