Concrete – mix latex paint into concrete

The final color of the paint depends on the ratios of the different pigments in the paint, and those ratios won't change once the paint is mixed. The storage instructions on all the interior paints that I have say nothing about high temperatures, just to protect from freezing which I believe would cause the paint to de-emulsify.

That said, a paint can's lid doesn't form a perfect seal, and higher temperatures are going to cause volatile chemicals (including water) in the paint to evaporate faster than normal. (I've noticed that paint that has been left open for a while and thinned with water behaves differently than a can of fresh paint -- I can't define exactly how, but it just doesn't paint as well). However, given that it can take weeks for a coat of paint to cure fully under normal household conditions, if the can is sealed well, my SWAG is that it would take years before you'd notice a change in the paint.

Paint on a concrete walkway will never last very long, and adding sand would definitely make it chip faster. The correct way to do it would be to stain it. I would use a good stain instead of what you get at the big box stores. Then seal it. Concrete sealer you can get anywhere. You can add some sharkgrip to it for the non-slip you are looking for.