is a peculiarly American form of horse-racing, and I commend the following site to your attention:

http://www.trotting.com/what-is-trotting/

In the article, it clearly states that the standard of the day in question in this posting, the mid-1800s, was "2.30-2.31" for a mile. That being so, I'm wondering whether to agree with Colin, who is obviously on the right track (ouch...), or to post my own answer, as these horses are clearly a little faster and can cover the mile in LESS than 2.30 (2.29, etc.), rather than specifically in "2.20", but "in the 2.20s", i.e., "between 2.20 and 2.29".

I started writing this before David posted his reference, but was interrupted.

I have found this expression used with two different meanings:

1. A horse that can run a mile in 2 minutes 20 seconds
2. A horse that specialises in running sprint races of 220 yards (a furlong).

I have not posted the second as an alternative, because I think the first, Colin's suggestion, is more likely to be what the expression means in this text.

References:
1. This is an article from an American newspaper, the Lewiston Evening Journal, dated 3 June 1880. It is talking about yield of wheat has risen: it was once 20 bushels per acre and it is now 40. How is this possible?

"in the same way that we have gone from a six foot to an eight foot ox, from a three minute horse to a two twenty horse."
http://news.google.com/newspapers?nid=1913&dat=18800603&id=F...

Oxen have got bigger and horses have got faster. A horse used to run a distance in three minutes, now it runs that distance in two-twenty. The distance is obviously a mile. So the fastest horses around 1880 were two-twenties, capable of running a mile in 2 minutes 20 seconds.

2. The second meaning occurs here, in a later text: "Boy's Life" magazine from May 1932. A boy in the story has lost a short sprint race (100 yards). He has a slow start. Someone tells him:

"You're not a short sprint man at all; but a two-twenty horse. That trigger start--it wouldn't count against you in the longer dash"
http://books.google.es/books?id=jHibnoOKgZoC&pg=PA15&lpg=PA1...

The longer dash was the 220 yards (nowadays 200 metres).

This is clearly a metaphor, but it may reflect an established expression; horse sprint races were once popular. The usual expression here was a "quarter horse", meaning a horse specialising in the quarter-mile:

"Quarter Horse:
The Quarter Horse, the oldest American breed, was developed in Virginia in the 17th century. It evolved from an amalgam of British breeds to be the chunky, compact horse we know today. [...] Early settlers loved racing them over a quarter mile (hence the name) through scrub or the middle of the village. By 1656 Quarter Horse racing was established, preceding the Thoroughbred and its oval tracks featuring longer distance racing by several years. Once Thoroughbred racing became all the rage, Quarter Horse racing experienced a sharp decline and was quickly abandoned. [...] Quarter Horses are faster than Thoroughbreds, but run shorter distances. The classic distance of a Quarter Horse race is 440 yards (400 m), but races are run from anywhere between 100 and 870 yards (800 m)."
http://www.ushorse.biz/racing-race-horses.htm

Note, however, that it says short sprint races went out of fashion when thoroughbreds came in, and this had already happened by the mid-nineteenth century. So I think it's unlikely that "two-twenty horse" means a horse specialising in 220-yard races in this text.

So I'm pretty sure these "two-twenties" were 2' 20" milers, the fastest horses of that period. "Down to" doesn't mean "in descending order of merit"; it has the chronological sense of "down to the present day".