We seem to go through this topic every year.
My post from 2005 covers much of what is being asked here.
The general rule for peas is that they can go in when the soil is workable. Mudding in will cause all sorts of problems as the roots will not develop properly even if the seed does not rot. This year mine were planted on March 17 but would have been a day earlier if I had come home in time. I planted the first spinach on March 14. It started coming up yesterday along with some volunteer arugula. Both the peas and spinach were covered with clear plastic film to warm the soil and stabilize moisture, neither too wet nor too dry. This had some benefits with the blast of cold rain and snow we got. You must check the plastic daily for seedlings coming through as they are easy to cook under this micro greenhouse. Planting spinach or peas after April 15 is likely to reduce yields as they will not have full production before heat does them in. Spinach and pea seedlings tolerate temperatures in the upper twenties very well but really hate the upper eighties at any age.
The big secret for cool-tolerant plants is to have soil with a lot of organic matter so tilth is good over a wide range of moisture levels. Clay with a high organic matter content will drain well even without using raised beds. My main garden does not use raised beds while another place I have gardened has raised beds but with lower organic matter. The good soil was workable weeks before the raised beds. At home it was hard to tell which portions had been spaded in the fall as all of the soil was very workable. The spinach followed arugula that produced way into November until it was hit with ground-freezing cold and snow and so could not be spaded. Some space where lettuce is going in this week was in Italian dandelions or cutting celery last year and again could not be spaded because they were producing so far into November.
The effects of Lake Michigan are a very important consideration. Within a few miles of the lake in Chicago and near northern suburbs the lake buffers both very cold and very warm temperatures. The last typical frost is much earlier than in the western suburbs while the latter have very much more warm weather in May and June. Lincoln Square is a great place to grow cool-season plants planted early while warmth-loving plants like basil, tomatoes, peppers and eggplant need to be planted later than further inland because it is just too cold for them even though using last frost dates would lead one to plant these vegetables earlier in Lincoln Square than inland. Gardening near Grand and Harlem for a couple decades has shown material differences in spring and fall compared to Lincoln Square even though the distance difference from the lake is only about six miles.
Rooftop gardening or gardening near masonry walls are very different animals from gardening in open ground for which the knowing the microclimates is critical.