I don't understand the construction. Why doesn't this sentence translate into we also need that swift horse
As far as I remember you are a native English speaker so you know the difference, but just repeat, perhaps for others: "We also need that swift horse." would mean some particular that horse which is also swift, so that swift horse.
We also need a horse that swift. means we want a horse which is that swift as something we probably can see or what somebody just told us about. Or as swift as the horse the speaker we are talking to owns.
Tak rychlého is literally so swift, so fast, so indeed we (také - also) want a horse that is so swift as something we know.
Thank you. I confirm I am a UK native English speaker and understand the distinction you have explained so well. I understand if také actually means so rather than that and is more of a comparison than indicative. I thought rychlého was an adjective describing horse.
It is actually an adjective describing the horse. I thing maybe the closest to the Czech sentence is "We also need such a swift horse." which I think is very different from that swift horse which would be that we need that particular horse *toho rychlého koně".