One downside of being locked up in the ice for thousands of years, if you’re a virus, is that your host’s immune system will go on evolving without you. Yes, it might lose the ability to quickly recognise the virus (and so be more susceptible to infection) but the pressure to actively lose this recognition ability is normally tiny.
The flip side to this is that the most successful viruses are probably the ones we never find out about because they have evolved alongside us to just sit there hidden in our cells, spreading slowly but not doing anything destructive enough to kill the host (or cause the host to kill itself). A previously benign virus might lose this ability simply because it was recognised as foreign. I doubt this would turn into a pandemic though.
NB: I’m not a virologist so if anyone wants to dispute this please do so!