Cryogenicists are still trying to figure out how to freeze our bodies so that we can be resuscitated intact at a later date, but viruses don't necessarily have this problem—they're simpler and, on a cellular level, much more durable. Say hello to pithovirus siberium, frozen for 30,000 years in Siberian permafrost but still as deadly as it ever was (to amoebae, anyway):
Pithovirus siberium isn't going to hurt us, and it's a pretty safe bet that most of the other long-frozen viruses released by climate change will prove equally harmless to humans. What we need to worry about are viruses that might still be lying intact in frozen human corpses—and the longer a group of corpses has been frozen, the less likely it is that we'll have any significant immunity to the virus that killed them.
Case in point: the gradual melting of the Italian Alps over the past 20 years has revealed the mummified bodies of World War I soldiers. These bodies aren't going to be the source of a global pandemic, because the soldiers died during wartime for the reasons you'd expect—gunshots, exposure to the cold, and so on. But if the body of a human who died from a long-dormant virus thaws out (and it just as easily could), we might have something to worry about.