If you're in Maine, your planting season should be similar to mine here in NH.
Read up on potatoes. I'm planting some for the first time. I think the manure you want to use is too fresh for potatoes. Sometimes the manure three feet down hasn't composted and is still too mucky. I've decided my soil is still too cold for potatoes. We seem to be having a late spring. I'm holding off for another couple of weeks. Google "how to grow potatoes" and read as much as you can.

I make lasagna style beds starting with wet newspapers covered with layers of things like grass clippings, chopped up leaves, etc. Usually these are started the year before so they can continue composting in place. This has added a lot of organic matter to my garden. The soil is nice and loose. Perhaps you can find some old leaves from last year you can till in. Our leaves get chopped up when my husband mows them up into the collection bag on the mower.

I planted sugar snap peas 2 weeks ago and do not see any germination. I forgot to water and pre-soak the seed so I might have to re-plant. Usually I am planting spinach in early April but I have a row that wintered over plus more in a high tunnel. Around here there are people who don't plant anything until Memorial Day weekend to be safe from frost but there is a lot that can go in sooner except when the soil is cold, germination is poor.

I've linked to a manure application table from the University of NH. It says 35 lbs of horse manure per 100 sq feet. I found a source of well-composted horse manure (kitchen scraps and bedding were added over the winter and pile was turned) on Craigslist. I may have added 2". It's black. The table is for a moderate application. Note that it says to double the amount for heavy feeders like potatoes but cut in half for light feeders like beans and peas.

You may want to wait another couple of weeks for planting depending on how cold your soil it. People seem to agree that if you wait until it's warmer, plants grow more quickly and soon catch up to those that were seeded earlier.

I splurge on fish emulsion/fertilizer liquid to use for watering transplants like tomatoes and peppers. I rarely loose a transplant. Read as much as you can. If you can find a used copy of Crockett's Victory Garden, it's a month-by-month guide of what to do in the garden. It's based on a tv show that was filmed in Boston. Keep in mind you might be a month or 2 weeks different because of being further north. Your library might have a copy.

Here is a link that might be useful: manure application table

totally agree with defrost. Plus fresh horse manure contains weed seeds. If not well composted, you will be dealing with a field of weeds instead of potatoes. And fresh manure can burn plants.

Agree with all the other posters about fresh manure. All the weed seeds that were not killed in the plot plus the ones the horses ate will come up in your garden and you'll be growing a field of weeds some of which you may not have in your yard. If you can't find aged or composted manure there are a few things you can add this year.

If you have leaves in your yard from the fall run over them with the mower and till them in. If you have a newspaper shredder till in shredded newspaper. Then buy some compost and till it in where you plan to plant the rest of the garden. Potatoes will make do without rich soil for this year. If you have lots of space make a small lasagna garden. When you mow the lawn all summer sprinkle the grass clippings around the garden. They will act as mulch and rot down into soil.

For this year add some commercial fertilizer to the garden.

As for time to plant--Nothing will sprout and grow in cold soil and you'd likely be a couple of weeks behind this year just like the rest of North America. Those frost free dates are only a guideline. You have to go with what the weather tells you is the right time

For next year, add your manure (fresh or composted) in the fall and till or turn in. That way your garden will be ready for early crops as soon as the soil is ready. For this year, you can probably safely add a very small amount of the manure you have to your garden bed (1/2" deep) since if it's steaming, it's partly composted. Break it up into small pieces and mix it in very well. Water it well if you don't have rain, and by the time you are ready to plant, it should be fine.

In cold soil, it's always best to presprout to decrease issues with rotting, IME. I planted peas 2 weeks ago (I am quite close to Defrost) that I had presprouted by soaking overnight and then sitting with a damp towel over the dish for a few hours and they are now about an inch high. (I'll plant another set this week to extend harvest.) I chit my potatoes, setting them in an egg carton for a couple of weeks and letting them green sprout (just let the eyes barely start) so that when I set them out they will be ready to go. I also often predig my potato trenches or holes, since even when the surface soil is warm, several inches down it is still quite cold. Letting some heat in a bit deeper seems to help. When planting I only fill in enough soil to cover the potatoes with an inch or 2 of soil at first. When they sprout a couple of inches then I fill in to just below the leaves and continue adding soil or compost as they grow.

Here are directions for potato planting from two of my favorite sources, both of which happen to be in ME.
Johnny's Select Seeds:
http://www.johnnyseeds.com/Assets/Information/GrowingPotatoes.pdf

Wood Prairie Farm, which includes green sprouting info:
http://cdn.woodprairie.com/downloads/Growing%20Guide.pdf

As others have said, this is a late spring, and jumping the gun won't end up getting you a quicker harvest. Spend time now getting your bed ready and plant in a couple of weeks for your cold weather crops.

Here is a link that might be useful: Chitting potatoes (ignore the photo which is NOT of chitted potatoes)