An important part of learning to fly is learning to fly in all seasons. As for weather, book more lessons knowing that one third to one half will be cancelled. Check with your flight school for when this will be a good strategy.
In my opinion, flying once a week for an hour is an inefficent way to learn. If only weekends and no early mornings / late evenings are possible, I'd book two hour slots morning and afternoon both Saturday and Sunday.
The cash flow is steep, but you can get your license in a few months for less total money instead of a few years as happens with many.