Just to add on here to the good advice given:
Your OP has a couple "points" that should be cleared up.
First, when you use the term "Exposure Compensation", that refers to an adjustment you make in Av, Tv or P mode to move the exposure from what the camera deems is "correct" (where the needle is centered). When you do this, the needle will no longer be centered -- it will stay "fixed" at the level where you set the exposure compensation.
But, using EC in one of those modes does not set the exact exposure, but only the exposure relative to what the camera is metering at a given point.
So, in one of those "semi-auo) modes, if you point the camera at the ice and dial in the +2/+3 EC, at that point you will get a good exposure for the whole scene. But then, if you want to shoot the guy in the black jersey, you will focus on him and your camera will meter him, taking the black jersey in, and will set the exposure to "medium" plus the EC you have dialed in. The meter needle will read +2/+3, whatever EC you have dialed in. When you then look at the shot, you will have everything overexposed.
This is why Manual exposure can be helpful here -- you will have a single exposure for everything. The black jersey will have a "needle reading" of perhaps -2 EV, which is proper for a dark garment. The yellow jerseys will have perhaps a +1 EV reading, because they are lighter than "medium", although not as bright as the snow.
Now, some people do prefer to shoot in, say, Av, and to use the EC to adjust "on the fly", and that's fine as long as you understand what you are doing -- if you are shooting the black jersey you adjust your EC to the negative, but if you are shooting the yellow jersey, you adjust to the positive.
Do you get what I'm saying?