Let's take a good look at Fluttershy's cottage. We see it a lot, but never a kitchen, or even a 'food room' for that matter. Only the fireplace/hearth right by her front door, which has pots and pans around it. Why else would the pans be there unless she has no stove?
Why ponies get refrigerators (in fics) is also beyond me. Their technology is a little behind ours, with some exceptions. I'm not saying artificial refrigeration doesn't exist. As in our world, it existed for something like half a century before it was commonplace for an ordinary household to have an electric refrigerator. And of course magic messes up everything when it comes to pony tech. But we've only ever seen one 'refrigerator' in the show, mind you the word 'refrigerator' was also synonymous with 'icebox' before electric refrigerators became the norm. Anyway, the only food-cooling apparatus we've seen was in the library (conveniently placed when Spike needed a bottle of ketchup) and it looked suspiciously like an ice-powered icebox of old. In fact, go back and look at that, I think I spy a block of ice on the bottom shelf (why it's on the bottom is beyond me). Hence the whole 'ice service' thing, based on our past tech and the show's canon.
Also, one of the most important reasons for home refrigeration is to preserve meat. So obviously, refrigeration probably wouldn't be as big a deal to ponies then. But Rarity seems to think it's important that a pony's milk not turn into yogurt overnight.
We've seen stoves in the show, but then again the term 'stove' is broad and could also describe a wood or coal fueled stove. Even so, maybe Ponyville has gas piping to each home in town. Or maybe just electric stoves. Or each house has a propane tank. Or magic. *snort snort* But we don't know. And even electric and gas powered stoves were fairly common in homes way before electric refrigerators were. Anyway, the cottage is way out in the middle of bu-fu, so it's a little hard to say whether Fluttershy would have any utilities that houses in town might have. Assuming they even have electricity or gas. Or maybe they pipe magic into houses to power appliances. Who knows?
And I don't know much about the toy lines, maybe they've suggested that she has a kitchen of some sort. I'd like to point out that the toy people don't know jack. They think Applejack and Big Mac are MARRIED and their children are Applebloom and GRANNY SMITH. So the toys don't count.
Either way, she don't have a kitchen.
So… I rest my case.
:3