If there is no food available a horse needs 6 pounds of food per day. Since the site also said a mule could carry 150-160 pounds (and a horse maybe a little more) this would mean a lot of pack animals if there is no food availabe. On your main horse you wont be able to carry much beside yourself and equipment from what I see. Water seems a little more problematic than food even. Another side suggested a horse could go 25 days without food and 14 without food and water... but I am pretty sure you wont be able to ride it hard then, so its kind of irrelevant. I don't think grassing or feeding food you brought makes much difference timewise, since you only ride 8 hours max anyway.
So going with a horse might be more of a hassle than going without, at least over the larger distances of 1000+ miles. Today pilgrims used to walking seem to cover 15-25 miles per day as well, but of course they don't carry a lot of things, since most of the roads they take have a rest place every few miles. If you are halfway good hunting your own food its probably still an option, even when it slows you down considerably.
... actually imagines travelling a bit monotonous when I first calculated the numbers, but maybe it is more challanging than I though after all.
