The distinction between hot/cold is kind of irrelevant. There's exchanges and there are wallets. Funds on an exchange are held by a 3rd party -- if they go bankrupt or get hacked or whatever, you could lose your money just like if you had any funds at FTX. They are holding your funds not you.
Funds on a wallet are held and controlled by you. Some wallets are just apps on your computer or phone, some require the use of a kind of physical USB device. All wallets will generate a password seed phrase for you (usually 12 random words). These words are all you need to recover your funds in the event of your PC blowing up, you lose your USB device, etc. That's why you shouldn't have any worry about whether the wallet software/provider you choose will still operate in the future. Guard the seed phrase carefully. That is all you or anyone else needs to access all the funds in your wallet.
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Aside:
As for hot vs cold, that's just more how you treat your funds. If you're always sending funds to/from books, you probably have your wallet always online on your computer and logged in. In theory you're more likely to get hacked and lose your funds if you use your wallet like this (i.e. hot = always logged in and connected to the internet). You could still create a software wallet, load it with funds, then log out of it and delete the software. Now it's "cold" and all you need is the seed phrase to access the funds in the future, even via a different wallet software.
The reason I think hot vs cold doesn't really matter is ultimately to access a 'cold wallet' you'll have to load it up and connect it to the internet, so if your device does have some kind of malware or something, you're still vulnerable at that point. Or, in the case of Trezor, if you connect it after years of inactivity and then either don't update the software or DO update the software but by going to the wrong site and downloading a trojan instead, then you might be vulnerable.
