Hi Michael,
Thanks for visiting the Disney Parks Moms Panel with your question.
Disney's Polynesian Village Resort is lovely, with a tropical theme as well as fantastic proximity to Magic Kingdom. On a recent stay at Walt Disney World, my daughter and I also did a horseback trail ride at
Tri-Circle-D Ranch. It was a really nice way to spend some time relaxing at Walt Disney World.
In order to get from Disney's Polynesian Village Resort to Tri-Circle-D Ranch at Disney's Fort Wilderness Resort & Campground using Disney transportation, you could take a boat or monorail to Magic Kingdom, and then a boat to Disney's Fort Wilderness Resort & Campground. At this point, you would need to take a bus from the Settlement area of Disney's Fort Wilderness Resort & Campground to the front of the resort for the area from which the trail rides leave. While this is possible, I would leave at least 90 minutes for this travel. You should check with cast members at your resort for how early transportation begins on the day that you are traveling, which will depend on what time Magic Kingdom opens.
Another option is to simply take a taxi from Disney's Polynesian Village Resort to Disney's Fort Wilderness Resort & Campground. These two resorts are geographically quite close to one another, so the taxi ride should be short and relatively inexpensive. The taxi will drop you off at the front of Disney's Fort Wilderness Resort & Campground, which means that you will be right where you need to be for your horseback trail ride. There should be taxis available at the front of Disney's Polynesian Village Resort, and if not, you can ask a cast member to call one for you.
Please do let us know if you have any further questions, Michael!