It shouldn't hurt it to run it. Its a fan cooled 4 stroke very similar to a briggs and stratton motor. I would however add some wheels to the skid frame. I would check the track periodically and make sure its not getting to beat up.
I have a wheel kit on my son's Z120 also. I agree that you should get the rear skid wheel kit. My six year old loves riding it on the lawn. It's a little bouncy without any rear shocks, but I saw that Polaris is coming out with a mini M-10 for the 120s!(M-6.3) Dual coilover front and rear shocks, coupled, and ready to rock and roll. It's in the new Snow Tech.
Here's a pic from last winter. You can see the rear wheel kit mini bogies on the slide rail.
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