I'm not sure how practical that would be, especially for someone with significant heating requirements.
My average winter-time heating requirements are pretty low, perhaps 50,000 BTU per day and perhaps 75 days a year when I need heat. 50,000 BTUs is roughly 14.65 kWh, per day, x 75 days. Say 4 million BTUs or 1.2 MWh. Someone further from the equator could easily require 5-10x as much stored energy.
We get a monsoon season during the summer so I actually produce more on an average day in February than I do during July.
Spring and fall are when I produce the bulk of my surplus electricity, and many days I do produce 15-16 kWh surplus. How much calcium oxide would be required for storing that much energy? How much space would the stored chemicals require?
I come up with 110 tons of calcium chloride for my modest heating requirements, but perhaps I did the math wrong.
FWIW I'm not a good candidate for this type of system since I produce
enough energy during the winter to run a heat-pump anyway. But for someone that could use some type of long term heat storage, I'm guessing this would be prohibitively expensive.