I have no further information, but tend to agree with Brad that there's a good probability that there may be a conflation of two different men. The given name Thomas was prevalent with early Horton lines; in fact, a Thomas de Horton of Devon is the first documented Horton I know of (Hundred Rolls, 1273).
But I just want to add that dropping of the initial "H" really isn't a misspelling. And I'm typing this out quickly, while I'm thinking of it, because I may want to expand it for the WikiTree Horton Name Study.
The most common variant of Horton is Orton, and either can be found spelled as Horten, Orten or, less frequently, with that double-T as in Ortton. Phonetically, it's easy to see how it came about. That initial "H" sound, technically a "voiceless glottal fricative," has an interesting history in the English language.
The "H" at the start of a word was typically spoken, or aspirated, in the prototypical Germanic languages. But in Northern Germanic languages, which led to Old East Norse, the aspirated "H" was sometimes dropped. Likewise, a significant change between Latin and Early Old French was the dropping of the consonant. So Old English and the language as spoken in England by the early Saxons had, in most instances, an aspirated "H."
In 1066 William brought with him his language, Norman French, which had mostly dropped the aspirated "H." We see that silent "H" in many of the words that English borrowed from French during that period. Examples are heir, honest, hono(u)r, hour.
So in the last centuries of the Middle Ages, England grew up with a schism in language that had the aspirated "H" as one of the central players. Evidence can be found in texts as early as the 13th century that the phonetic dropping of the "H" had found its way into written materials. And speaking of players, we can find puns sprinkled through many of Shakespeare's plays that use the dropping of the "H". Unexpected insertions of an aspirate "H" also came to be and, while still on a terpsichorean bent, a memorable "H" passage there is in George Bernard Shaw's 1913 play Pygmalion (probably better known later as the musical My Fair Lady) when Eliza Doolittle is taking elocution lessons and give an initial try: "In 'Artford, 'Ereford, and 'Ampshire, 'urricanes 'ardly hever 'appen".
Examples of how "H" was added to words, and stuck, come from some French words absorbed into Middle English, like habit, harmony, and horrible; the French didn't include the prepended "H."
Still today we struggle with that darned "H." The British English pronunciation of herb includes the aspirated "H." American English retains the older version with the "H" silent, but we definitely aspirate it for the proper name Herbert or its hypocorism Herb. Even the name of the letter itself is pronounced differently in English dialects: haitch or aitch. And for some, like me, attention is always required in written syntax because we can lapse into old habits of putting "an" instead of "a" before certain words that at one point had phonetically dropped but then regained the aspirated "H," words like historical, heroic, hypothesis. Of that, the original Fowler's Modern English Usage tells us: "[S]peakers who like to say an should not try to have it both ways by aspirating the h." But an (which derives from the Old English one, dropping its purely numerical denotation by around 1150) is definitely on the wane in English style guides.