First sensible statement you have made.
The speed of travel is changing if you slowly come to a halt.
nothing needs to.
If you can apply X amiunt of grip over Y distance, starting at Z kinetic energy, the total energy you have to climb the hill is Z+X*Y
If you have grippier chains, its Z+2X*Y
If the actual thrust from the non chained tyres isn't enough to get started up the hill from a stop, you are screwed there anyway.
The key is you hit the hill moving..if the thrust is not enough to maintain speed up the hill, you will eventually stop at a distance governed by the above. If you have more grip, the distance will be longer, and if its enough to clear the crest, you are home and dry.