You are not over thinking it. These are the types of things you must think through, otherwise, you get blasse and don't bring the epi-pen.
For ski racing, I suggest a waist carrier, which can be worn under her coat. Her body heat should keep it warm enough.
For the beach, some people put it in the cooler. There are also water-proof carriers available (though neither my son nor I wear our carriers while actually swimming). I usually wrap an epi-pen in a plastic bag and put it in my waist carrier while walking the beach hunting for shells. Since my son is allergic to insects, we have to have an epi with us while doing that, and he was little and tripped a lot on the beach, so I carried the epi-pen there.
Others may have better ideas.