Why is a bride and groom called so? This relates to horses. What's the link?

The word "bride" has meant "woman about to be married, or just married" ever since it was first borrowed into Old English (as "bryd") from the Germanic languages back around 1000 A.D. The adjective "bridal," incidently, did not originally just mean "pertaining to a bride or wedding," as it does today. The "bride-ale" was the wedding feast (Old English "brydealu"), so called on account of the vast quantities of ale served.

Meanwhile, back at "bridegroom," the original form of this term for the lucky chap was "brydguma," combining our old pal "bryd" (bride) with the Old English word "guma," which meant simply "man," and which was a completely different word than "groom."

What happened then was that over the years, people stopped using "guma" by itself, but were still using the term "brydguma." Eventually people began substituting the more familiar "groom" for the by-now obsolete "guma," and "brydguma" became "bridegroom."

Forgot the part about relating to horses:

The bad news is that no one has ever been able to figure out exactly where "groom" came from. It just showed up one day back when folks were speaking Middle English, and none of the words in other languages that looked like "groom" could be proven to be relatives. In any case, "groom" at first simply meant "young man" or "male servant." But because young male servants were likely to be put to work taking care of horses, the meaning of "groom" shifted over the years to mean a male servant caring for horses, and then, by extension, his duties. "Grooming" eventually broadened beyond horses to apply to any sort of hygiene or preparation, such as "grooming" a candidate for office.

According to Times Dictionary, guma is Old English. The Old Norse and Old High German are very similar.