I'm not seeing any stats in the PHB. What is the limit that saddle bags on a horse can carry? If there's not any definitive stats would it be OK to assume that each saddlebag is similar to a backpack?
I couldn't find any definitive stats either, but given the cost and weight, you should assume roughly double the capacity.
For the math on why it's double despite not being double the weight, essentially it's because volume increases faster than surface area. If you assume the same thickness and density of material, you can use the weight of the object as an estimate of it's surface area. You can then solve for the sack's volume by assuming it to be a sphere, and while it's impossible to know the units, the volume you get with a surface area of 8 is 2.14 compared to 1.05 from a surface area of 5.
Barring further rulings on the matter (such as from the DMG), I'd say it's quite reasonable to project the carrying capacity of a backpack onto a saddle bag. You could definitely account for them being bigger as well, but realistically, a horse's carrying capacity is between 2/3 and triple that of a typical adventurer (480 vs 150-300). Thus if you take the weight of an adventurer, and then add on his gear, and then add saddle bags, you aren't going to want much more than the volume of a backpack additionally attached.
That said, an unladen horse may be able to carry more, but the saddle bag still has physical limits. I'd set these either at or slightly above that of a back pack. It's definitely in the realm of DM discretion though because the rules are silent. Whether he chooses a verisimilitudinous answer or an abstraction will of course depend.