Single horse vs single elephant, win or draw? This is depends on the position of elephant. If the elephant and the king are on different side of flank, then this is a draw. However, if the elephant and king are on same flank, then Red would able to win the game (as below).
The trick is Red horse must control the center line and must not allow elephant moves to the other flank.
Red moves first
1. H1+3 K4-1 2. K5+1 K4+1
3. H3+2 K4-1 4. H2+4 E3-1
5. H4-3 E1+3 6. H3-4 K4+1
7. H4-6 K4-1 8. H6+7
Red would have gained the elephant and wins.