Will your horse allow you to mount and dismount from either side? Mounting from the left is just tradition. Soldiers would mount up on their horses left sides so that their swords, anchored over their left legs, wouldn't harm their horses' backs.
But you're trail riding, not heading into battle. Make sure your horse is comfortable with you mounting and dismounting on either side. You never know when you'll encounter a rocky cliff, a mud hole, or other trail hazard. Alternating sides also allows your horse to use muscles on the right and left sides of his spine equally, which helps his back.
Here's how to get your horse comfortable with right (off) side mounting: (1) Lead him from the right side, asking him to stop, and turn in each direction; (2) stop him, and practice walking toward his right side, directly toward his heartgirth; (3) when your horse appears calm thus far, saddle him, and place the tip of your left boot in the right stirrup; (4) if your horse seems concerned, repeat the previous steps until he's used to the experience; (5) if your horse stands calmly, step up into the stirrup, but be prepared to kick out your foot and jump down, if necessary; (6) if your horse remains relaxed, swing your left leg over the saddle, and gently sit down; (7) repeat your off-side mounting and dismounting until it feels comfortable to you and your horse.