No, not tension. It won't help, and may lead to damage to the saddle.

To harden leather... well, in my experience, every time a saddle gets soaking wet and dries out again, it dries harder than before.

I'm not going to claim this is a good idea, but consider the following as a thought experiment. You could fill a bucket with clean water and dunk your saddle in it for a few hours, long enough to get really wet, then let it dry out again. If you do this, you will notice that the water has turned dark brown, suggesting that some soluble substance has been removed. Probably not good in the long run, but as I say, in my experience, the saddle subjected to this treatment will dry harder than it was before.

Baking the saddle for a half hour in your kitchen oven, at the lowest possible setting, for a half hour or so, will also tend to harden the leather.

Anything you do, to harden the leather, is basically speed-aging the leather. You are making it older; and the effect, whether it turns out to be good or not, cannot be undone.