I need more USB ports but my hub is USB 1.0. If I connect my mouse to it, is there any drop in performance?
You're probably using USB 1.1 rather than USB 1.0, unless your hub is really old - USB 1.0 was short lived and hugely uncommon
Practically there i would think that there shouldn't be much difference - the data transfer for the average mouse should be significantly less than the 12 MBit/s maximum speed of USB 1.1 or even the fallback 1.5 MBit/s speed of low speed USB (though no one really seems to have hard data on that), and the extra performance of USB 2.0 is really cause USB started being used for mass storage (which earlier USB versions weren't very good at, they were supposed to be a versatile way to plug in peripherals primarily).
Now, if you have some fancy, USB 2.0 requiring all singing all dancing supermouse, maybe JUST MAYBE it might not like being plugged into USB 1.1 hub, and act up, but its hard to tell. If you DID have such a mouse, get a better hub
ALl that said this is one of those things that has too many variables to give a definitive answer, so i suggest spending the 30 seconds or so actually trying it.