I bought web hosting under FastComet and they have a free
Let's Encrypt SSL service that comes with the package. There is an option to include the domain's subdomains (webmail,webdisk,cpanel) to install the certificates to, but I don't know if I need to do so.
There is no reason not to do it.
If you go read your emails through
webmail.example.com do you want anyone to be able to read them also, and maybe change them in the path? If not, you need HTTPS, and hence you need a certificate (either specifically for
webmail.example.com or a wildcard one of
Browsers are more and more leaning towards HTTPS everywhere, so any
http:// resource will soon become highly suspicious.
In a world nowadays where you can easily have free and automated certificates, there is no reason not to do HTTPS.
Of course the above is a simplification, since after getting a certificate you still need to configure (or have someone configure) your webhosting correctly. It does not buy much if you have a certificate but still do TLS 1.0 for example, this would be vulnerable to an active attacker.