How can I prevent the intake vent for an on demand water heater from getting plugged?
Picture of the vents would help. The way I've usually seen them installed is with a 90deg elbow on the intake so that it points down. That would prevent snow from clogging it.

The exhaust vent pipe usually has a 90 deg elbow so that it points up. You can get a rain cap for the end of it to keep rain/snow out.

Looking at this document from your manufacturer it shows one of the vents elbowed to face down like I indicated the other one isn't.

After seeing the pictures of your vents it looks like you can elbow the one on the right and then get a hooded cap for the one on the right. Something like the Noritz PVT-HL looks like it might work.

Then you can install a tighter mesh to keep the wasps out.

By the way, have you tried those wasp deterrents that look like nests? I haven't but they seem to have good reviews.