Is it possible to win the first fight in Grubbins on Ice?
Solution 1:
I lost this battle like you did, and I believe it's intentional that you lose. The story carries on from there. However, some people have reported winning it, and the game just carries on the same way as before.
The reward for winning this battle is 7500 xp.
Solution 2:
If you want first-hand experience, I finished it (barely). As the others have said, you get EXP for finishing the fight and still get pushed off the cliff. An NPC later mentions something about you losing, so they're definitely working on most people losing that fight.