From the Mt. Rainier Visitor Association blog:
The Paradise area is filled with wildflowers this time of year, and the fields are filled with bright-spotted beauties while the trails are packed with eager photographers and outdoor enthusiasts. In can be tricky trying to find any solitude at Paradise this time of year, but Deadhorse Creek Trail and the Moraine Trail to the west side of Paradise are good options for getting away from the crowds.
The easiest way to begin is to park in the lower parking lot at Paradise, which is southwest of the Visitor Center. This 2.5 mile hike is moderate with wide trails that are paved for a portion of the walk. There is a 400 ft elevation gain that takes place mostly within the first .75 mile, with the middle section of the hike flattening out, and the descent on the return.
From the trailhead at the lower parking lot, take the well-marked trail due north, bearing right at the first Y-intersection. If you park in the main Paradise parking lot, head up the stairs to where most of the trails begin and cut hard to your left. You’ll be paralleling the Visitor Center on the Avalanche Lily Trail and you’ll cross the Alta Vista Trail, and then you’ll come to the T intersection of Deadhorse Creek Trail where you will take a right.
Once you’re on Deadhorse Creek Trail there is no way to go wrong, as there are many other trails that intersect Deadhorse. You can turn around if you are tired or let your feet guide you towards the glacier, a field of flowers, into the valley, or towards a creek. If you continue to follow Deadhorse Creek Trail, after about 3/4 of a mile you will have the option to turn left onto the Moraine Trail.
The Moraine Trail is not a loop, but it does take you right down to the “snout” of the Nisqually Glacier. Most visitors skip this option as the trail is unpaved and easy to overlook. The Moraine Trail is a great place to veer off the more-frequented Deadhorse Creek Trail, dip over a rise and head down into the valley where the Nisqually Glacier sits. You can find a few rocks to relax upon and soak up the quiet of your own corner of Paradise before retracing your steps on the Moraine Trail and rejoining Deadhorse Creek. If you choose to turn back now, the round-trip hike would be just under 2.5 miles. I recommend taking a left on Deadhorse Creek and continuing on a bit higher.
The Deadhorse Creek Trail meets up with the Skyline Trail after a half mile, and you could either take a right on the Skyline Trail to head back towards the Paradise Visitor Center Parking Lot, or you could push on another .2 miles for a spectacular view from the Glacier Vista trail. Either way, once you begin heading down the Skyline Trail you could also opt to switch over to the Alta Vista Trail after a .5 mile. At this point, head wherever the beauty calls to you or wherever there are less people to mar your view. All trails had back to the Paradise Visitor Center Parking Lot, or if you cut to the right (west) on the Waterfall Trail or the Avalanche Lily Trail, they will bring you back down to the lower parking lot.