Many times out on the trail we come across a tree blown down on the trail. For this reason, I bring pack saw on every trail ride. My current pack saw is an 20" Fanno cut-on-the-pull with an Outfitters Supply leather scabbard. I find it's easy to use and about the ideal length for clearing smaller trees and limbs from the trail.
How to hang a pack saw on your saddle.
I prefer to tie my pack saw handle with the rear saddle strings and then secure the blade under my leg. However, the pack saw scabbard has a versatile design that would allow you many options. Whichever way you choose, remember to offset the added weight of your saw by loading your horse saddlebags or horn bags heavier on the opposing side.
I almost always take an axe with me on any trip longer than one day. I prefer a camp axe for chopping firewood, and there are some cases where they just work better than a pack saw. Since I generally take a pack mule with me on longer trips, I usually attach my camp axe to the outside of my pack load, offsetting the weight with other gear or by packing the opposing side that much heavier. You can, however, easily attach a camp axe with a sheath to your saddle. An axe sheath is usually designed with rings on either side, which can easily be tied to you saddle strings. This puts the axe at a nice angle to slide the handle under your leg.
Do I really need to carry a pack saw or a camp axe?
The obvious answer here is for windfall blocking the trail. It is not always possible to go around a windfall, nor would you necessarily want to get into that habit; the new trail you would create only adds to the erosion of a potentially fragile area. It is better instead to simply clear the trail. The standard rule for clearing trail is to clear 4 feet out from center on either side. Clearing trail is a good Leave No Trace practice. You will be helping out the Forest Service, the Backcountry Horsemen or any other local riding associations as well as any of your friends that may ride that trail later. And it is good exercise for you while giving your horse a break.
Besides clearing trail, a pack saw or camp axe could save your life if you get into a bad situations. I have heard stories and seen situations where a horse has gotten stuck after a wreck and the only way to get him out was to saw through the limbs holding him down. Additionally, if you have any sort of accident or get into a bad situation that leaves you stranded, especially in bad weather, the ability to chop firewood and keep yourself warm can mean the difference between life and death.