Securing a new wooden floor to a steel framed horse box
You need to consider the spacing of the steel frame.

If the floor, for the loads you expect to put on it (you have an idea?), is not to bounce or sag then you may need to add joists. You don’t mention any and horses tend to be heavy with a small hoof print so it may be ok if you are replacing like with like.

If your new flooring is different then you should check if it will be suitable.

I would fit joists - fix them to the steel and the floor to the joists... but that is my opinion, based on doing a truck for 3 musicians years ago... storage, fold out kitchen, fold out beds etc