When it's time to start the irrigation system up for spring in more northern parts of the country, the first rule is to check that the ground is no longer frozen. For people just moving into these areas, it might not make any sense that the ground itself can be frozen when it's nice during the day, but that is what happens in areas that regularly see below-freezing temperatures. The moisture in the soil and rock freezes up, making it difficult to plant anything or even dig a small hole. For irrigation systems that use underground pipes, the problems are even more pronounced as frozen ground can damage sprinkler systems that start up too early in the year.
First, when the ground is frozen, it doesn't mean it's immobilized. The frozen water inside the ground can expand as it freezes and heave anything in it upward. For sprinkler pipes, that means potential cracking and leaks -- only you wouldn't know it because everything is frozen, so you wouldn't see water leaking out. If you wait until the ground has thawed before running water through the pipes, you'll be able to see if there are any leaks you need to take care of.
Frozen Pipes and Ice
Even if the pipes are in great shape, any water that runs through the pipes will likely freeze. You'll get a very low-pressure flow out of the pipes and possibly end up with a chunk of ice expanding inside the pipes, leading to damage. You need to be sure that nothing will freeze, at all, when you turn on the sprinklers and let water run into the pipes.
Making Frost Damage Worse
Even if you could get water through the pipes without it freezing, all you'll do is contribute to frost damage on the surface. If the ground is frozen, water could very likely freeze once it hits the ground, if it hasn't frozen in mid-air. Chances are there isn't any grass left above the surface, but seeds or dormant grasses that would normally start growing again in warmer weather could sustain damage.
If you're about to move to a colder region or have just arrived there from a warmer region, lawn care is a bit different, and you need to take precautions when starting up an irrigation system after winter. You may want to have an irrigation company come out and evaluate your yard to ensure that the house you bought has the best type of irrigation given the home's location and the yard's size. You can have a new system installed if you find a style that suits you better.