I plan to switch hosting for one of my sites that is on a subdomain of my hosting company site, i.e. mysite.currenthosting.com. Is it possible to change the hosting but keep the subdomain by pointing it to a different IP on new hosting, of course with the help of my current hosting?
If they allow you to edit the DNS - set up the A record for mysite now to the correct IP address and you really should not experience any downtime with that one.