I decided to grow my own tomatoes from seed using no electricity to see if it could be done. To be fair - you can NOT grow tomatoes from seed without some sort of protection.
I grew my tomatoes from seed in a recycled milk cartons inside a cheap plastic greenhouse in zone 4.
To read all about how it worked out - check out this series of articles:
Growing Heirloom Tomatoes without Electricity
19 Tomatoes and Counting
Winter/Spring Seed Starting without Electricity - Part 1
Winter/Spring Seed Starting without Electricity - Part 2
How to keep indoor plants and seedlings for getting leggy while grown in a window
How to grow seedlings in winter in northern climates
But you can grow tomato seeds in the ground under cover (no milk cartons needed) as long as you know WHEN to do it. The answer is simple and most likely relates across all zones.
Plant your seeds under cover of cloche, tunnel, cold frame, or greenhouse when you see your asparagus plants popping through the soil. Asparagus only emerges when the soil is warm enough. A cloche/cold frame tends to add 10 degrees Fahrenheit to the air and soil within it, and the temperature needed for asparagus is just about 10 degrees less than the temperature needed for tomato germination.
So if you watch your asparagus (assuming you have asparagus and if you don't you should grow it. It's so delicious fresh from the garden!) you will know when to plant your seeds under cover.
Your seedlings will benefit from natural light (no leggy window grown seedlings!) and they will harden off easier since they will have to deal with some nightly temperature fluctuation. Since they are in the ground where they will stay, they will also put down longer tap roots so they should be stronger and more resistant to water fluctuation throughout the growing season.