Please tell me is it safe to exchange Bitcoin on Ledger Live? I see they use a third party provider.
Even though my coins are in cold storage, can they be frozen during the exchange?
You will probably get better rates if you used those exchanges directly without going through Ledger because the company charges a fee and earns a small percentage for everything you exchange. These instant exchanges all have terms that say that your coins can be frozen if they deem them "dirty" or their blockchain partners assign a high-risk score for them. In situations like that, you will be asked to do KYC, provide source of funds, and/or any other information they ask of you to get your money back or perform the exchange.
I suggest you check
KYCnotme and see if you can find a more private and KYC-free way to perform your swaps instead or using Ledger and their suggested third parties.