I cannot recommend running Server 2003 at this day and age. Your on the verge of not receiving any security patches shortly.
Likewise, Server isn't designed to be rebooting constantly, it should happen maybe once a month at the most for patching, and that would be during off-hours anyways. Regardless, Server 2012 boots decently fast, even on HDD's, assuming you don't have a ton of roles running. Hyper-V kills boot times the most as it has to power up/down a bunch of machines.
I'm with JD. it's 2013, forget Server 2003. I curse and groan every night I have to do anything on a 2003 server. I almost can't bear it anymore. And it's not like migrating is a chore anymore, so that's not an excuse at all in my mind for any admin to be holding on to some relic of what once was