Learn Croatian: Volimo se sanjkati nizbrdo.

Nizbrdo is actually an adverb meaning downhill, formed by fusing the preposition niz (down) and the noun brdo (hill). Because it is functioning as a single-word adverb here, it doesn't decline for case. However, if you wrote them as separate words, niz brdo (down the hill), then brdo would indeed be in the Accusative case. Both are perfectly fine to use!

Why is the reflexive pronoun se placed between Volimo and sanjkati?

Se is a clitic (a small, unaccented word), which means it strongly prefers the second position in a sentence. Since Volimo takes the first spot, se jumps in right after it. Even though the dictionary form of the verb is sanjkati se, saying Volimo sanjkati se sounds unnatural because it pushes the clitic too far back in the sentence.

Is the verb sanjkati se built directly from the noun for a sled?

Yes! The Croatian noun for a sled is sanjke (which is a plural-only noun, much like scissors or pants in English). Croatian frequently turns nouns into verbs this way, so sanjkati se simply means to do the action of using a sled.

If nizbrdo means downhill, how would I say uphill?