We're switching the DNS over to XX's servers for our website.
We have loads of subdomains and they have their own IP addresses. Will switching over our DNS affect our subdomains?
Considering that DNS is how all those subdomains get pointed to the correct IP address then yes switching your DNS provider for the main domain will affect them. However as long as you put all the appropriate settings for them on the new DNS servers then they shouldn't really notice the change.
It really depends on how the responsibility of the zones are handled.
I'd bet your situation is probably (1) - if you were a (2) you should already know it.
Remeber that you may need to update the reverse delegation also (i.e. the address => name mapping).