Simplicity need not imply clarity; I can make nothing of your question. Please elaborate:

Did you mean "Because the world was too hot?"

or                  "Because the world was too dry?"

or                   "because water no longer froze (or melted)?"

or                    "because water only froze into dirty looks instead of crystals?"

or what?

All those would carry different consequences you know!

Changing as few as possible of the laws of physics, what would be the effect on life on earth - particularly human life - if there was no such thing as snow? Well eviltony changing the laws of physics so that the water did not crystalize under earths current atmosphere. Would in fact change earths atmosphere. It would even change the structure of the sun once formed. It would change the nature of the formation of the big bang and the way the universe expanded. We would have to look over all these dynamics right from the big bang right up to the formation of an earth. Then we would need to be able to take into account the life formation process, and given our understanding of that process, do know enough to calculate if it would start with an alterted unstable form of h2o because that is essentially what you want is something that doesn't stabalize or crystalize in lower heats. But further more because you have changed the laws of physics themselves as stated above star formation is changed I would think that because you are modifying the stability of h2o particle. You are also modifing the stability of every molecule in the universe. You have modified star formation as well, in a way that increase randomness ie (temperature) would rise. Because of this following the ideal gas law PV = nRT , You are a going to either increase preasure or increase volume or both. From the above that our star would form differently it would also mean that it would provide more momentum in the form of heat to dust particles in the early formation of the solar system, this is due to number reasons coming together you have given a possibility for more volume to the sun and you have given a looseness to the dust atom in your need for instability of the water molecule, the shape of the sun being different means that it will be most likely be emiting more energy into the early formation of the solar system, so think of this as more solar wind thinning the mass of what would one day end up being earth. Already by this hypothesis of modifing the laws of physics following a possible hypothetical flow of universal expansion and sun formation, we have a smaller earth. So I would ask you what other changes are we likely to see in this universe we have created?      

Well Tony, I was thinking of trying harder, but I don't see how I am to improve on Matt's little effort. Fiddling with "laws of physics" is like removing a single ball bearing from the bottom of a pyramid.

Now --- do you still want a "better answer"? I trust it is becoming clear to you that so far you have lacked a certain indispensible prerequisite, and I correspondingly hope that you are working at making good the shortcoming.

clearly, if snowflakes didn't form, then the water-ice at sub 0°c would start to form ice balls (the 'crystalline' flake form is bypassed).  assuming polar bears, penguins, kiwis and other arctic and antarctic life forms do live in freezing environment most of the time, they won't be affected.

however, man wouldn't be able to enjoy skating.  another thing would be avalanches may not form as quickly.  still, ice could break as in glaciers.

i don't see any other thing being affected.

however, this is my opinion and i may be wrong.  please correct me if i am.