I've encountered only ogród dendrologiczny, dendrarium and arboretum. I've never heard of a more specific term for pine trees only. "Ogród botaniczny" on the other hand is a more general term, including a collection of all sorts of plants.
I've googled "pinetum" in Polish texts, but it was a part of Latin names referring to natural formations, such as las iglasty or bór - but in Polish such formations are typically named by the dominating species of trees, like las sosnowy, las świerkowy, las jodłowy.