"How would we pro-rate the portion related to keeping the house cooler in the spring, summer, fall, and most of the winter, warmer in January/February, and the gas and water for daily bathing?"
That is exactly the question.
The cost of installing and maintaining the solar panels, A/C system, etc. are not allowable medical expenses. I believe the excess cost of running the system at 64F (instead of 74F, for example) is an allowable medical expense in your situation. However, if audited, you need to show the IRS some reasonable basis for calculating this excess cost. I'm not sure how you can do this. For example, if your son is ever out of the house for a day, you could set the system up, get your daily usage, and compare it to a similar day when he is at home and the system is set down, to get the percentage difference. And the cost to run the A/C on a 75 degree day would be all excess due to medical reasons, while the cost on a 90 degree day would only be partial excess. Or, you might be able to compare your electric usage with neighbors who have similar sized houses in the same geographic area and electric supplier. (Maybe take an average. The utility company might have this info or some of your neighbors might volunteer to share their bills.) Or, you might need to talk to an HVAC company, or a company that does home energy audits, or even the electric utility. There are devices you can attach to your electrical panel that can measure the electric usage of different appliances in your home (to separate the cost of AC from the cost of lights, computers, refrigerator, etc.) but those devices by themselves won't tell you the excess.
The IRS wants you to have a reasonable method to allocate the cost, but it does not have to be perfect. However, it should be something you monitor and keep records routinely, and not something you guessed at the night before your audit.
Unfortunately, I don't believe the costs of ice skating are deductible. Exercise programs for general health are not deductible unless they are a specific treatment for a specific condition. From your description, the ice skating is for general health, not a specific treatment, so the fact that it is the only exercise he can tolerate and is expensive, is not enough to make it deductible. But that's just my opinion.
The IRS guidance on medical expenses is here.
https://www.irs.gov/forms-pubs/about-publication-502
