There is twenty horses.
Is there an error in this sentence? Twenty is more than one, so there are should have been used.
Why the use of there is with plural?
As @StoneyB comments, OP's cited usage is probably an error. That's to say few if any (reasonably competent) native speakers would accept it as "valid" except in very contrived contexts.
But it's worth pointing out that - particularly in relaxed colloquial speech - the contracted form there's isn't so strictly constrained. You can read John Lawler's explanation of why there's is so common, even with plural subjects in that answer over on ELU (essentially, it's a "frozen construction" - within which context subject/verb agreement doesn't always work). Thus it's "okay" to say...
1: Get me a beer, will you? There's two bottles in the fridge.
(This version would never involve the uncontracted form.)
Other contexts where the singular verb form can reasonably be used with a plural "subject" (even when not contracted) include...
2: He lied when he said he had no money. There was over two hundred pounds in his wallet.
(In this context, over two hundred pounds is being treated as a specific single amount of money)
3: You should eat some fruit. There is an apple and a couple of bananas in the bowl.
(Would usually be contracted, but some native speakers agree to the first item in the list anyway.)
Grammatically, the sentence is incorrect. However, the reason some people may say or write this is because of the word "twenty" which is close to the verb. I think there is general confusion as to whether "twenty" or other number determiners should be plural or singular.
"How many horses are in the barn?" "There's twenty."
I feel it should be "There are twenty."
If we replace "twenty" with the word "brown" the mistake would not happen: "There are brown horses." not "There is brown horses."...at least in writing...speaking is another matter.
From a purely textbook perspective, that is absolutely ungrammatical. The subject (horses) and verb (is) don't agree in number. This sentence construction is an example of an inverted sentence, where the subject of the sentence appears after the predicate. Rearranging the sentence into a more typical construction yields:
Twenty horses is there.
Now, it is more obvious that the subject and verb disagree in number.
As for why people make this mistake, I can think of a couple of reasons. Because of the inverted construction, it can be a bit hard for people to think ahead and choose the proper verb to agree with the subject they've likely already chosen. English speakers are used to thinking subject-verb-object in their construction, so flipping it around can cause some confusion.
In informal spoken English, many people fall back on familiar phrases like "there's" even when it's incorrect. On reason, is the that the logical contraction for "there are" is "there're," which is nigh impossible to pronounce. People will be able to understand you either way, but technically, "there's twenty horses" is grammatically incorrect. If you use the contraction you're fine since no one really cares that much about perfect grammar when they're using contractions. But broken up, "there is [plural]" is terribly incorrect.
It is an error by pure grammatical rules.
Recently (probably within a few decades), the tendency to use "there is" as an idiom regardless of the number of the following noun phrase can be observed in the speech (and writing in media and nowadays on FB and the likes) by the members of the public less concerned with "correctness" or "propriety" of what they say or write.
There is women who...
There is websites...
There is pictures...
are numerous, and if one searches the Web for them, probably outnumber the correct ones (but I haven't checked).