Thank you all for the thorough replies! I’m sold on cold storage now. I just purchased the Ledger Nano S.
Let’s say most hardware wallets will give you much better security than any custodial wallet which is actually a crypto bank that has partially secured funds, and besides, you are not using the full potential that Bitcoin offers you - and that is to be your own bank.
I would just correct you about calling a hardware wallet a
"cold storage", because every crypto wallet that has contact with the Internet can't fall into that category. To understand what cold storage is, visit this link
Cold Storage.
Also, don't be fooled that with the purchase of such a device all problems and challenges with the security of cryptocurrencies disappear - you must take the issue of backup very seriously (24 words) and always be careful when sending and receiving transactions (check if all information matches on the computer and hardware device screen).
It may be too late now, but everyone should be very careful with their
personal information when buying such devices.