OSRIC 2.2 refers to pack animals such as cart horses but does not elaborate on the rules for these. What rules should I use for pack animals in regard of how much load they may carry? Additionally, are there any rules for animal drawn wagons/carts?
Unlike many other “retroclones,” OSRIC is not actually made to be played on its own, but rather used only as a reference for adventure and supplement designers who want to indicate compatibility with AD&D but, for whatever reason, want to avoid using the name. The existence of OSRIC allows these publishers to state compatibility with “OSRIC” instead, which means it's compatible with AD&D without saying “AD&D” anywhere. (Since TSR was famous for suing anyone who said their stuff was compatible with AD&D, even though that's legal, the idea is that such frivolous lawsuits can be avoided by not using the name at all.)
As a consequence, it has many rules missing, because the reader is assumed to be really using AD&D books.
In this case, the book you're missing is the Monster Manual (1977). The entry for "Horse" (p. 53) gives load limits for full and half movement speeds for various types of horses; the "Mule" entry (p. 72) lists limits for mules.
If you don't have access to the Monster Manual, you're not out of luck yet. Because OSRIC is based on the d20 SRD, you can use information from the SRD to fill gaps like this. For example, the SRD entry for Horse says this about heavy horses:
A light load for a heavy horse is up to 200 pounds; a medium load, 201-400 pounds; and a heavy load, 401-600 pounds. A heavy horse can drag 3,000 pounds.
In a similar manner, you can refer to the d20 SRD text on carts and wagons. The Transport subsection of the Equipment section and the tables for overland movement speeds provide some basic information. As for how much a beast can pull in such a device, that's not a function of the transportation, but of the animal's basic carrying capacity plus the rules for pushing and dragging capacity: anyone can push or drag five times their normal capacity, so just take the carrying capacity of the animal or animals hitched to the wagon or cart × 5 to find out how much can be loaded.