Try to visualize what a "melted" and then a "melting" snow man ought to look like. Different parts of him might need to "fall off," such as his carrot nose, which would be a separate part of the animation (and must therefore be a separate part of the model). The texture of the snow might change. Holes might need to develop in him. The shape of the spheres might need to squash. And so on. First figure out what visual elements you need and what you want to achieve; then look at various ways to make them.
When you want to "generally squash" something, like putting a character into a glass bottle that's too small, a lattice is a good way to do it. When the lattice is made the parent of the object that is to be deformed, movements of the lattice can be animated and the object will follow suit.
And this particular technique, being just one of many, will serve to achieve one of the visual effects you've decided you want to obtain. It thus solves one of the problems you've identified and posed for yourself.
You can make Mister Melty just as simple an animation or as complicated as you wish. Since you're learning, start with simple and then "try things." When you produce one version of the animation, also practice the art of looking beyond the "it looks like crap!!" 
response and ask yourself, why does my eye say that "it looks like crap?"
In other words, when you make a change to the scene and your eye still finds it wanting .. as it always will .. practice seeing critically. Practice the art of observing, as though you were somehow a disconnected third party, what it is about what you have done that you find to be the least close-to-the-mark; and considering, what of all possible changes you could now make to it to achieve the most positive results. For one thing, this will help keep up your encouragement as you learn. You won't feel (as much, anyway), that "it's not right (and I don't know why, it just looks wrong) and I don't know what to do to fix it." As you build up your arsenal of 3D techniques, also build up your practiced eye.
It can also be great fun to try three different ways to melt Mister Melty. How would Wile E. Coyote do it? How would Tom & Jerry do it? What if he got sucked into a vacuum cleaner and shoved into a steam boiler? What if he got turned into dry ice and collapsed in a heap of dust? You can try five or six different sick, fun things with Mister Melty and keep your interest up.