None of the most problematic rodents here hibernate completely. Only ground squirrels hibernate, but they are rare, and tend to avoid home gardens and refined landscapes. Some other rodents are less active through the cooler parts of winter, but never completely stop eating, chewing and digging up what they want from our gardens. Many will become more active with warming weather.
Gophers are the most destructive rodents right now. They might still be excavating the mud of last winter from their tunnels. They will find plenty to eat as warming weather stimulates root growth of their favorite plants. Young gophers are growing up and leaving home, to excavate more tunnels and consume more vegetation elsewhere. They are more numerous now than they will be all year.
Squirrels are not so industrious. For now, they are destructive only if they dig out recently planted seedlings and bedding plants, or eat flowers and freshly emerging foliage. They should otherwise be temporarily satisfied with acorns that they hid late last year. They will become more of a problem as they eat ripening fruit, nuts and maybe vegetables later in summer. Some might chew bark.
Rats are sneakier than squirrels. They are not as destructive to ripening nuts and stone fruits, but do eat some of what falls to the ground. Although not a problem for the garden, well fed rats infest adjacent homes, where they cause serious damage. At this time of year, rats sometimes ruin citrus fruit. They eat the pulp out from the rinds of oranges and tangerines, and the rind off of lemons.
Rodents are nearly impossible to exclude completely and safely from gardens. Poisons are too dangerous to be practical around the home, particularly if there are dogs or cats anywhere nearby. Traps are safer and effective, but require diligence. Also, some traps are difficult to set. Each type of rodent exhibits distinct characteristics. That which controls one type is ineffective for another.
Sanitation and vegetation management deters some rodents by depriving them of sustenance and nesting sites.
Tony Tomeo 
Oh my goodness, your photo reminds me that our resident woodchuck family will soon be waking up at work. For years, I was able to garden there in peace with them but the last year or two they have gotten truly voracious. Oh well. New garden year, new garden challenges.
Karla
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Woodchucks are much bigger, and excavate more! I am glad I need not contend with them. Gophers are bad enough.
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I would admire their persistence if I didn’t hate them so much. Rabbits are the worst, at least around here.
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I worked with jackrabbits only once, and they were horrible! I think that rabbits are even worse. I saw them roaming freely around a town near Seattle. They were numerous, but too small to stew.
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Not clear on the difference between rabbits and jackrabbits. I’m familiar with jackalopes.
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Jackalopes are the WORST! Jackrabbits are not as bad, but might be worse than common rabbits in some ways. They might excavate more, and they probably eat more roots. They are rabbits who live in deserts and chaparrals.
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Tony, is that a picture of a gopher hole? I think I may have one as the hole is larger than others I have seen. I also have voles, which enjoy several roots of my perennials.
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Both gophers and voles are regional. I mean, the species or variety of gopher who live here might be quite different from those who live there. Voles tend to appear in phases here. We may not see them for many years, and then, big herds of them move through. However, gopher holes tend to be larger than those of voles, and are rarely as neat. They are only open like the one in the picture while they are actively being excavated. Vole holes are mostly clear and open, and sometimes in groups. Anyway, if you see what seems to be an unusually large vole tunnel, it could be that of a gopher.
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