You'll get more information at https://hammockforums.net/ where it's all hammocks, all the time.

I started out using a foam pad in my hammock, but it never worked well for me. Staying on the pad was a pain and it took away some of the comfort of being in a hammock in the first place. most of the nights I tried using pad, I threw it out of the hammock halfway through the night. If you're successfully and comfortably using a pad already, you may not need to make any changes. It's true that a pad can be useful, too, if you have to go to ground, but I gave up on it. Also many people have found that a normal pad is too narrow for hammock camping, and on the forums you will find methods people have employed to get a little more insulation at the shoulders.

Originally I had a Hennessy hammock, so I bought the insulation kit that Hennessy makes to fit them: basically a compressible, foam sheet that hugs the underside of the hammock, and a nylon (?) sheet that went outside of that to provide a little wind protection and the ability to put more items in between the pad and the under-sheet, like a space blanket. I found that set up to be very versatile. The outer cover alone provided a little insulation for cool, but not cold, nights, and adding a space blanket to the set up got me comfortable at near freezing temps. It packed down small enough for bike travel, too. Smaller than my blue, foam pad, and maybe comparable to my old, inflatable pad.

When I replaced the Hennessy, I got a double-layered hammock. I knew I eventually wanted an underquilt, but didn't want to spend the money right away, so I got a thin, closed-cell, foam pad: Thinlight Hammock Pad - 1/4" It was lighter and thinner than my old pad, packed a little better, and slid between the layers on my hammock. It was thinner, wider, and molded to my body better the old pad, too. The shape and the fact that it was held in place between the layers of my hammock meant that it stayed in place better. Still, that was a place-holder item, and I now have an underquilt. It's easier to pack than any pad I've carried, but, because it's a synthetic insulation, rather than down, it doesn't pack super small. I crammed it into a 5 liter bag the other day, although I expect with a compression sack, I could get it a bit smaller. The underquilt is definitely the ultimate in convenience and comfort for me. I understand the versatility of having a pad that can also be used on the ground, and, if that is working for you, you may not want to change anything, but I've been very happy since ditching my sleeping bag and various other insulation attempts and moving to just an underquilt for the outside and a camping quilt for the inside.