Newbie question, I guess. I want to get a cold wallet for increased security. I also want to start using hardware 2FA (e.g. for e-mail). I see that Ledger advertises 2FA capabilities ('FIDO U2F') on their Nano range. Is there a downside to e.g. buying a Nano X and using it for these two totally different functionalities? If so, what is a better option?
Short answer: yes and no.
If you're regularly inserting the device into a USB port for non-wallet purposes, it's not quite as "cold" as it would be otherwise, so there's a non-zero hypothetical risk increase, but ...
The frequency with which you have to insert your U2F device should be relatively low for most web applications (you're generally only prompted for the key when you're either logging in from a "new" device, or if you're doing something security-sensitive like changing your password, changing U2F keys, etc.)
A potential compromise: acquire an additional inexpensive U2F key, and use that as your "daily driver" (though it will probably be used much less often than that). This allows you to minimize non-wallet use of the wallet, but still have the wallet available as a second factor in an emergency, etc.