I want to ask you whether my plan to mix tyres are worth it.

I want to put winter tyres on the front (front wheel drive) and keep summer tyres at the back for the winter months. I then want to swap the winter ones to the back during the summer months to try and get more mileage out of them. And them swap them back to the front next winter.

Hopefully get two winters out of them. Will this improve the grip I have on a wet and or icy road and do you think there will be any negatives in doing this?

So is it worth the extra cost and effort? This is working with a limited budget of course, hence not getting four winter tyres.