With the new Horse UI, you can ride and untamed horse and before it kicks you off you can open its UI, put on armor and a saddle, and it will be instantly tamed.
MC-16207
Instantly Tame Horses
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Reproduced this. No need to put the armor on, just the saddle is enough. Also, the horse isn't tamed. When I took the saddle off horse threw me away and behaved as an untamed one.
Edit: also lead can't be used on untamed saddled horse, unlike on the tamed ones.