Let's take just one house
I think solving the problems of a candy city is a bit too much. First we need to solve a single house.
There exists water resistant sugar. Thanks to fat proteins encapsulating the sugar you get hydrofobic properies. This can be used on any outer layer that needs water protection in a frosting form. Roofs, exterior walls and patios will be regularly coated (every month? Really depends on the coating, it's thickness and the erosion from weather and living). This will reduce some of the greatest dangers of your mostly sugar houses. If you're thinking "what about sinks, pipes and sewers?", you'll be glad to know those commodities were either a hole in the ground with possibly a shed on top, or non-existent/incredibly rare. Water from wells will do, though not wells from sugar I wager.
As an alternative you can use gum. Looking at how dehydrated gum on pavement can last for years, even with people walking over them (which seems essential for it to bond with pavement at the start) and being in all weather, it is a long lasting solution. Seeing how it isn't affected by water at removal, it seems watertight. Just compress it tightly on the surface and let it dry. Possibly compress it several times during the drying process.
To build you need strength in the build materials. You can't just grab some random hard candy (M&M?), slap some gum in between as mortar and call it a day. It should last. It lead me to an article that wanted to answer:
Objective measurement of physical properties of a hard candy confectionery tablet under crushing local compression force
After some conversion I saw that the hardest tablets had a compressive strength akin to standard concrete. 3626 psi against the standard 3500 to 4000 psi. A side note here is that the test might be in favour of the candy, as well as the small shape influence the test... Even if it's only three quarters as strong it's suitable to build with individual hard tablets, graciously giving them the benefit if a doubt that they're not actually worthless as building material. There might be some others, like those incredibly hard round candies, but I suspect that they actually cannot withstand as much force as you might think.
For mortar I would use gum. It is shown that gum can be terribly difficult to remove after dehydration on the street, so it can be used to stick all the little tablets together.
You can decorate the inside and outside walls with whatever you like. Just add the (clear?) Frosting on the parts that can get wet.
For windows you can use the hydrofobic sugar for candy glass, or use normal candy glass and use a clear coating over it. I'm giving the tablet gum combination the benefit of a doubt they have the structural strength that they can have windows. Just to be sure, make them small and round.
Separate floors I wouldn't attempt. Even though the walls might be created, I cannot think of a candy with the structural strength to hold up a floor. You could look into having several layers of candy cane, but be mindful it likely flexes too easily, leading to breakage of it's internal structure.
On the ground floor you can cover it with any candy you like, as long as it doesn't make walking impossible.
This also poses a difficulty for the roofs. Even if people aren't walking on it or placing furniture, it should hold the weight of rain and, more importantly, snow. To solve this, we might be able to use slanted walls as roof. Although we can start the roof after the straight walls, I would suggest slanting the walls slightly from the ground up, giving the whole thing a sort of high hut feel. The slant should be slight to make as much use of the compressive strength of the tablets.
Right now I would go for an empty, not candy covered bit of ground on the floor with just a chimney high above it. That way the heat wouldn't be directly damaging the candy. It would make it bad over time, but at least you have a working house with fireplace for a time before maintaining is required.
If you really want a fireplace you can try the following, but do take it with a grain of salt. The heat resistance is mostly meant for melting and has not been tested for open fire:
Granola bars, peppermints, fruit drops, sour balls and jawbreakers seem to have a good resistance to heat in extreme climates like Afghanistan inside cars or the direct sun without being refrigerated.
Roads and walkways
The roads and walkways will again be made of gum. It's reluctance to go away is highly prized in roads. The problem is that it'll likely get slippery after some erosion. You might want to renew the layer every so often, or have a team of road gnomes rough it up every so often. It'll help if it isn't like one enormous gum, but many individual ones so you can get some more surface area.
I skipped furniture, but I'm sure some creative solutions for these less demanding items can be found.
You can have rudimentary homes to create a whole village. Despite heavy reliance on just a few building materials, you can decorate the outside and inside with many different candies to hide this fact. This makes it a colourful candy village you might hope to achieve. As long as each non-waterproof candy in harms way is protected, you can place it anywhere.