Don't see why Cossacks should not have artillery with them. Tried to post a link but auto moderator says no. Look at Marks military history site ( Google it)

If the reformed infantry cannot fire at medium range, surely presence of cavalry to inhibit skirmishers is totally irrelevant?
In context of original question however, why should infantry not be able to fire at medium range if river only ankle deep? The skirmishers would wade in, use opposite banks ...