1) Crushing snow?

2) Warming up chocolate cookies (on shabbos hot plate) where the chocolate will melt?

3) Squeezing or shampooing hair?

4) Brushing your teeth?

Gemara tells us that one may not crush snow and hail on Shabbos for purpose of producing water.

From this we learn it's a problem to produce liquids by breaking down solids or even semi solids.

This would extend to crushing or warming ice, ice cream, butter, congealed fat or similar substances to cause to melt or dissolve.

These activities resembles the process of crushing grapes for their juices.

Included in this is chopping up juice concentrate so it devolves faster into water.

However you can put ice cubes into a liquid to melt, or even to crush into small ice fragments to put immediately into your drink, as not trying to produce water. 

That's the key, anything that is trying to break it down into a liquid is no good, so we don't stir a frozen cup of slush/slurpy.

Nor can one squeeze a hand full of snow if the intention is to turn it into water.

You can defrost a liquid at room temperature.

It appears that using whip topping from a pressurised can could be problem as whilst in the can it's in a liquid form and once it comes out it becomes like foam. Some are lenient but interesting to see another possible application.

In terms of melting margarine and the like, it's OK as long as most of  the melted liquid becomes absorbed into a solid substance.

Please note there may be an issue of "cooking" when melting ice cream or chocolate on a hot piece of cake. We are discussing the present issue of changing a substance.

If your hair becomes wet on shabbos you can't squeeze it to extract the water. Similarly shampooing is a similar issue. 

Way to dry it is to wrap a towel around your hair to absord the wetness.

You could use a dry toothbrush as long as done gently enough that it won't cause blood.

A wet toothbrush is a problem as it involves pressing and squeezing the wet bristles of the toothbrush against the teeth. Toothpaste is also a separate issue.