Irun through hills. i veer around mountains. i leap over rivers. and crawl through the forests. step out your door to find me. what am i ? ?

Hello

There are quite a variety of animals that fix your explanation, but the most common one is a squirrel. A squirrel fits your description, except i'm not sure about the jumping over a river. I believe for that, it might also be a stray cat.

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