Baxter park is a long drive from anywhere but one possibility to make at least part of that drive very scenic, and even longer, is to continue north on I-95 and follow directions to the North Entrance. Along I-95 the passengers will get a look at Katahdin and the Traveler Ranges which also pop into view as you proceed in rural Maine towards the gate.
The road is plowed to within a couple miles from the gate where you can park and likely bareboot over the snowmobile trail which otherwise is the perimeter road. About another half mile past the gate is the trailhead to Horse Mountain. When we visited in January the trail was unbroken. It is about 1.5miles to the "summit" with about 800 ft. of elevation gain and, being on the north slope of the mountain, I wouldn't be a bit surprised if you needed snowshoes. Along the perimeter road and the mountain you'll have good views of Grand Lake Matagamon. On the mountain there are some views east and likely Traveler but I doubt there is a view of Katahdin from there.
It's a long ride.
At the South Gate the best place to park is near Abol Bridge. Though you can enjoy a woods walk (maybe snowshoe) this area lends itself better to cross country skiing. You can do a loop that'll take you up a road near the power lines, to the unplowed road approaching the gate, up the perimeter road (a snowmobile trail, remember) and west at Abol Pond along Abol Stream Trail back to your car. I recommend this counterclockwise route if the strong NW prevailing wind is blowing because that first road is somewhat exposed and you'll enjoy it more with the wind at your back than in your face. Abol Stream, on the other hand, is comparatively sheltered by trees. While the views are less dramatic, they are pleasing and there's a good sense of remoteness to feed the soul.