He wins by default

Since the deer tried to cheat and got caught they both just agreed that the otter won, Oak thought that its not that big a deal, he'll just get his laundry or something for a day. But the otter didn't have that in mind at all.

"We are going to walk through the park together. We are going to be doing a good deed today! You gotta strip down and walk with me."

"Wait what?!"

"Simply, we will be giving out your clothes to anyone who wants them. You better strip now, or else..."

The otter didn't have much of a backup plan other than just tearing Oak's clothes off himself but the threat seemed to work on the deer as he replied

"Can I go into the bathrooms to strip at least?"

They walk into the bathrooms, into one of those larger bathrooms stalls before closing the stall door. The deer turns away from the otter and begins stripping off his shorts, shirt, socks and shoes before just standing in his undies. He hands off his clothes to the otter.

"Well... Here I am stripped down"

"Well then lets start!"

The pair walk out of the bathrooms, Oak's hands covering his bulge... He was wearing tighty whities. He was told to not cover up by the otter and from there kept his hands at his side. Immediately people saw the deer. They started their walk heading around the park, most people trying to avoid them. They walk around to a few benches with people on them, where the otter engages them in conversation where he attempts to give away the deer's clothing, Oak stands off to the side as he speaks just trying to wait out this bet... Eventually the first piece of clothing is given away, his shirt. It was newer, he had to recently get new clothes anyways, including the shoes. They weren't having much luck in that particular area so they head to some other benches. There they were able to give away his shoes and socks. Oak tried to hurry up the process, the quicker his stuff is gone, the quicker he's home. He personally tries to give away his shorts, really hyping them up, saying they are free, ultimately nobody took them from him. So the otter tried again, and was able to give them away, apparently wearing clothes helps out a lot...

They were now out of clothes, the deer thought. Although they kept walking around, it never crossed Oak's mind that he still had one piece left until it was too late. Eventually they start talking to this one lady, a bunny. She was the same one from earlier and she remembered how Oak was bugging her... So she went up to see why the deer was now half naked. The otter explains it and instantly she sees the only piece of clothing left on the poor deer's body. She says that she'll take it and soon after, Oak's undies had been pulled down and pulled off his feet. Oak's half-flaccid dick was exposed for a solid two seconds before he booked it out of there and ran to the bathrooms!

Now all he has to worry about is how to get home...