There's no way to protect skeleton horses from burning from direct sunlight without blocks above them.

As the title infers, skeleton horses have no way of protection unlike the zombie horse. The proper behavior should be that skeleton horses should be protected with horse armor like zombie horses. However, skeleton horses cannot wear horse armor, so they burn in sunlight.
Steps to reproduce:

1. Open up a creative world.

2. Set time to night.

3. Use /summon skeleton_horse ~ ~ ~ {SkeletonTrap:1} (for some reason skeleton horses spawned with a spawn egg cannont be riden?)

4. Kill theskeleton rider.

5. Left click the theskeleton horse to ride it.

6. Open up inventory and place saddle.

7. Set time to day and watch them burn.