Was cattle truly used in this more general form, and would someone in England in 1800 have used it to refer to horses? The quote above seems to say no.
1300 Cursor M. 6002 Hors, asse, mule, ox, camell, Dun {th}an deid all {th}air catell.
1523 FITZHERB. Husb. §37 Shepe in myne opynyon is the mooste profytablest cattell that any man can haue.
1577 B. GOOGE Heresbach’s Husb. (1586) 125b, The Camel is cheefly used in ye east parts, which some suppose to be the serviceablest cattell for man that is.
1604 E. G[RIMSTON] D’Acosta’s Hist. Indies III. xvi. 170 There are great numbers of cattell, especially swine.
1607 TOPSELL Four-f. Beasts 183 The goatherds of the countrey do give thereof to their cattel.
1697 DRYDEN Virg. Georg. III. 590 Is Wool thy Care? Let not thy Cattle go…where Burs and Thistles grow.
1741-2 Act 15 & 16 Geo. II, xxxiv, By cattle, in this act, is to be understood any bull, cow, ox, steer, bullock, heifer, calf, sheep, and lamb, and no other cattle whatever.
The OED also has a separate category for the “language of the stable, applied to horses”:
1733 FIELDING Quix. in Eng. I. iii, Your worship’s cattle are saddled.
1835 SIR G. STEPHEN Search of Horse ii. 34 All the disabled cattle of the summer stages to Brighton, Southampton, and so forth.
1886 J. S. WINTER In Quarters, To cast reflections unfavorable to…the color of their uniform, the class of their cattle.
So, yes, it seems that someone from England in 1800 could indeed refer to their horses as cattle.