Yes, you can lose your Bitcoin if you are too hasty in responding, this is definitely not only happening to Trezor as a cold wallet, other cold wallets must also get the same attack and try to trick all of us who have it.
So if you get any email from any party asking for a code or seed phrase from you, never share it, be it from a cold wallet or Hot wallet issuing company, beginners who enter this industry are much more easily fooled, so I suggest you be careful.
To any bitcoiner who has little or full knowledge about how Crypto/Bitcoin works ought to have known that the private key of a Bitcoin wallet is one thing that must not be shared to a third party, not even the company that owns the non custodial wallet. And as such, coming across an email requesting for your wallet private, you ought to have known that this is 100% scam, and avoid it, as I'm pretty sure it's only Newbies who are likely to fall for this scam, which is why I always advocate that whoever wishes to invest in Bitcoin, should also strive to invest in knowing it's basic security measures and how to prevent losing your funds due to errors.