I *think* the cold storage devices like Trezor and Ledger require desktop for set-up at the least, but not 100% on that, I've never researched any mobile-only functionality they might have.
A non-device based wallet like Mycelium works well on mobile only, I've tested this out, and I have it on my mobile now.
It just doesn't have that air-gapped device functionality like Ledger and Trezor. Mycelium has been around a while though and is well trusted, and they cannot freeze or control your bitcoin in any way that we know of, unlike the exchanges.
For example, when the canadian government recently introduced emergency regulations to be able to confiscate people's bitcoin (and cryptocurrencies), they were able to force exchanges to provide personal information and account details of their users, whereas proper wallet providers actually cannot provide that level of info, even if they wanted to. So it protects from hackers, but also government overreach. Most people would probably not see the canadian government as being any kind of bad actor, but it's still a good example to show what different levels of bitcoin custody actually mean, as other governments of our world might create similar regulation that comes from a more nefarious angle.
A non-device based wallet like Mycelium works well on mobile only, I've tested this out, and I have it on my mobile now.
It just doesn't have that air-gapped device functionality like Ledger and Trezor. Mycelium has been around a while though and is well trusted, and they cannot freeze or control your bitcoin in any way that we know of, unlike the exchanges.
For example, when the canadian government recently introduced emergency regulations to be able to confiscate people's bitcoin (and cryptocurrencies), they were able to force exchanges to provide personal information and account details of their users, whereas proper wallet providers actually cannot provide that level of info, even if they wanted to. So it protects from hackers, but also government overreach. Most people would probably not see the canadian government as being any kind of bad actor, but it's still a good example to show what different levels of bitcoin custody actually mean, as other governments of our world might create similar regulation that comes from a more nefarious angle.