Horse-pulled artillery actually did exist in the 19th century and earlier. However, as the emphasis was on mobility, they usually were lightly armored or unarmored.
From what I can tell, vehichle armor in the 19th century consisted of several inches of iron plate, backed by wood, and was used on ships and trains. The weight of such armor would be prohibitive for use with horses. However, this armor was made to withstand cannon fire. If you only needed to stop bullets or musket balls, you could do with a lot thinner armor, that might be more practical. Of course, if they're vulnerable to cannon fire, they wouldn't be especially useful as battle tanks. However, there are other roles for armored vehicles that might have a horse-drawn alternative.
Your best bet for function is something similar to an infantry tank, which is a relatively slow-moving tank designed to support infantry attacks. For this, you wouldn't want artillery on your carriages, since you'll be too close to the enemy for that to be of much use. You could still have small cannons, like swivel guns, that are lighter and designed as anti-personnel weapons. Also, breech-loading versions existed at that point, meaning soldiers don't have to get out of the carriage to reload them, which is a plus.
Armoring the horses themselves is impractical, at least if you do it directly. However, you could have them carry a sort of armored wall, like a mantlet, around with them. The design of this is a bit tricky, since it needs to be flexible or segmented to get over rough terrain, but you don't want gaps in the armor. Just having some overlap between segments should be enough. You will also want them to be able to turn easily, to be able to bring the guns to bear once in range.
The real question is whether this sort of vehicle or structure would be worthwhile. Anti-cannon armor is too heavy for horses, but a lightly armored version is still a fairly large and slow-moving target. Enemy artillery would be a serious threat. Still, if the vehicle stayed in motion firing broadside, it could be useful.