Do opponents see your alternate hero?

Solution 1:

Yes, other players see your skin instead of the default hero for your class!

They also hear the different voiceovers and emotes of course, that's what skins are for.

I can't really confirm your experience to be honest, I personally see them a lot when playing ladder. When the skins came out it was actually very rare to see a regular hero instead of the alternate one. ^^

I have to mention that I usually play on the higher ranks, so my opponents are playing for a longer time as well, increasing the chance that someone there bought a skin. In the lower ranks there are a lot of new players which probably don't want to pay money for cosmetic stuff when they can spend the money on card packs. However, this is just a wild guess but I think it goes to the right direction.