How much you'll actually save on your bills is a critical bit of information if you're downsizing in the interest of financial security. And the fact is, you can potentially save a lot.
When downsizing, chances are your new house is going to cost a lot less than your current one. Assuming you're able to sell your house for a reasonable price, you could put a huge down payment toward the smaller space and end up cutting your mortgage payment in half. You'll also cut your power bill, water bill, cleaning costs (if you have a housekeeper), landscaping costs, and your property taxes, which can be a huge one depending on your local tax regulations.
If you shorten your commute to work, you'll also cut your gas expenditures. In all, the savings can be substantial.
Assuming you can sell your house. In this market, that's not a given.