Hi,
I only have information about the Swedish stuff unfortunately, and that has largely been answered already.
As said above, Swedish artillery generally was painted a rather light blue with black metal fittings etc. The thing about grey seems to be a mistake. Swedish artillery was however painted blue with yellow metal fittings in an earlier period, although I would suspect that by 1813 the guns used would have been the model 1804 6-pounder, which seems to have been a rather efficient and light gun, which was probably available in some numbers by that time. That would definitely have been blue-black.
I dont know what information you have, but if it seems that the guns in question were obsolete Swedish guns (perhaps once replaced by the new 6-pounders in the Swedish army itself), it may possibly be that they could be painted blue and yellow.
Ive attached images of an older gun and a m/1804 carriage.