Slitherine

Looking at the 1809 Austrian list and it's VERY limited on the amount of artillery you can have. My question is can you purchase Horse Artillery and use it with a
Infantry Division?

Yes you can use Hose artillery in an infantry division . There is no general restriction.

5 guns total of foot artillery is not enough? Keep in mind you can attach artillery to 1 unit per division, it helps to make up for the lack of inherent skirmish capability and does not lose dice to enemy cav being near