I read it as someone (presumably a human) coming to the barn door to grab dinner (or take him to market to be someone else’s dinner) and the little piggy was the first barn animal to run to the door when it opened…because he was a naive, trusting little piggy. Little did he know, he was about to be slaughtered.
I read that as an animal running to the barn door begging for food. I don’t think that sounds ominous at all. Nonetheless, i think I’ve always understood the piggie going to market as going to market to be sold. (For pork chops). I’m shocked to learn there are illustrations from the 1800s of a pig going shopping. I would not have thought a nineteenth century child would anthropomorphize piggies that way.
Given the context of the whole poem, I think piggy went shopping, but that it’s likely meant as a double entendre, hence the OP’s question.
Ever read Bill Peet’s storybook “Chester the Worldy Pig”? My second/third grade teacher read it to us once. It’s a lovely yarn about a porker who concocts a scheme to get out of becoming someone’s dinner. There was one particularly memorable line:
To the farmer’s delight, after a couple of years Chester ballooned into a huge blimp of a pig; and one morning the happy farmer said, “Today this little pig goes to market.”
Check out the summary of the story linked above and make up your mind about it.
Yes, I can see this nursery rhyme being a double entendre—a sweet tale for small kids; a horrid tale for older kids and adults who read between the lines.
Example: In parentheses I give a sweet interpretation, followed by a horrid interpretation:
This pig went to market, (happy Pig went shopping / sad Pig was sent to market as food).
That pig stayed home; (Pig was too busy to go shopping / Pig wasn’t sent to market yet because he needs to be fattened up more before going to market as food).
This pig had roast meat, (Pig ate a nice roast meat dinner / Pig was fed roast meat to fatten him up OR Pig himself was roasted and sent to market pre-cooked).
That pig had none; (poor Pig didn’t get any dinner / lucky Pig isn’t being fattened up for slaughter…perhaps he’s the farmer’s pet).
This pig went to the barn’s door,
And cried week, week for more. (hungry pig went to the barn door and called for another animal to be slaughtered for dinner / naive Pig went to the barn door when the farmer called, then squealed when he saw the farmer’s ax).
It wouldn’t do for small kids to interpret the horrid version because they’d think you were going to fatten up their toes before chopping them off with an ax. But it could serve as a cautionary tale for older kids, and a funny tale for adults.
At least they didn’t put lipstick on the pig.
This is my way of thinking too. Pigs engaged in human activities like feasting on roast beef and living in homes, suggests that going to market was meant as ‘shopping’.
Darn, it’s been blurred out. 
I agree the quality of the pictures is not the greatest, but I can make out enough to know I really don’t want to see more. 
I assumed shopping because I was a little kid when I heard this. Had no idea that pork chops, ham, and bacon were all pieces of pigs. I thought hamburgers were made out of ham also. Eventually the idea of the pigs being marketed occurred to me, probably from some cartoon based on the Three Little Pigs.
Taking the rhyme a little further;
A good number of them! (Not that I think you doubted, just a chance to post some)
That top one might be early 20th century, I pulled it from my previous post but didn’t go back to date everything. The second from the bottom amuses me with her green-tinted sunglasses but is indeed from 1870.
In my hunt, I only saw one that was a pig IN a wagon, being taken to market, and I think it was a political cartoon or otherwise meant for adults. I can’t speak for the “original” intent of the rhyme but I think anyone calling it “went shopping” is accurate about the overwhelming intent of the children’s book publishers and illustrators of the past 150+ years.
Frankly, I’m amazed this conversation has gone this long without this:
That’ll do, pig, that’ll do.
The second and last of those appear to illustrate a pig going to market in order to sell, not in order to buy.
That doesn’t change the overall sense, of course. What appears to be being taken to be sold isn’t the pig, but produce.
Yes. This has definite shades of those sort of things. The latest one being “does 'Mac” stand for “mac’aroni” or is it an acronym of “Macaroni And Cheese”, which is pseudo deep when you first hear it until you realize that a common phrase is “mac and cheese” which would be “macaroni and cheese and cheese” and, more importantly, the dish of Chili Mac doesn’t even necessarily have cheese in it.
It’s a tickling game that parents play with small children. When it gets to the last line, they run their fingers up the baby’s leg and tickle its tummy. Somehow, knowing what’s coming seems to make it even more hilarious for the child.
Kids like to be scared a little while feeling safe at the same time. My mother used to threaten my sister and I with "tearing our arm(s) off and beating us with them. I only just discovered that this “commonly used threat” (I Will Tear Your Arms Off - TV Tropes) goes all the way back to Grendel in the poem Beowulf.
My mother did this with me too…except she followed through with the threat. 
Yours Truly,
Armless Tibby
Maybe he’s coming home with groceries! 
(You’re right, of course. The women pigs are all shopping and the male pigs are taking goods to market, it seems)
This is why I voted the “shopping” option. These are obviously anthropomorphized swine.
IIRC, Desmond Norris wrote about this in The Naked Ape (and probably other places too). Laughter is a way of relieving tension once you know you’re actually not being threatened at all.
This applies to people of all ages, not just children.
But pigs get all the leftovers, especially if they’ve dropped on the floor or something.