I bought a couple of REI brand air mattresses at their scratch and dent sales that leaked, patched the leaks and had good luck with them after that. The REI brand air mattresses I use are not noisy at all. One advantage of the REI ones is that the side tubes were a bit bigger, it was harder to roll off the side of the air mattress.

I have not winter camped for a couple decades, I was winter camping before Thermarest existed. I had good luck with a inch of open cell foam above a half inch of closed cell foam. In the morning the divot in the snow under me indicated that I melted less snow than the other guys that had less insulation under them. And my bag was down so I had virtually no insulation in my bag under me where I compressed it. An advantage of a frame pack like I was using for winter camping is that your rolled up pad could be enormous and not a problem because it was strapped on the outside of your pack, but for bike touring that could be a problem.

For bike touring I like air mattresses, they are much less volume than the Thermarest pads and I can put the air mattress in a pannier quite easily. But for backpacking where I can strap the pad on the outside of the pack, I prefer a really light weight shorty Thermarest pad instead of a full length air mattress.

One disadvantage of some air mattresses is that it can take several minutes to try to extract the air out in the morning. Consider that when you do your shopping, ask the staff at the store if they would mind if you tried to roll it up and see how long it takes to get the air out of it to roll it up.