We are planning a traditional Hungarian Goulash dinner, and apart from egg noodles, would like a vegetable side-dish to accompany. It's late October, and we'd prefer some seasonal ingredients if possible. What vegetable side dishes compliment a hearty, flavorful stew like goulash?
Sweet and sour red cabbage, cuts through the richness of the goulash very nicely - particularly if you cook some thin slices of tart apples with the cabbage. The vinegar also turns the cabbage vivid purple which also adds a nice contrast to earthy goulash. I found this recipe that is almost identical to my mom's (although I probably would opt out of using the clove):
[Possibly irrelevant-to-you aside: a true Hungarian goulash (as opposed to a North American or German or what-have-you goulash) is a soup. It includes a few root vegetables and possibly some "pinched noodles" (tiny little egg+flour dumplings) in the soup itself, but it is served with a hearty slice of bread or two, nothing more. So in that sense, the answer to your question is "mu".]
If what you're actually making is a meat stew with paprika (what in Hungarian would be called pörkölt), then the traditional accompaniments are either potatoes (with beef) or spaetzle (with any type of meat), and some sort of vinegary vegetable salad — either a cucumber salad, or some other vegetable dressed the same way as a cucumber salad (tomatoes, peppers), or pickled vegetables (sauerkraut-stuffed peppers, gherkins, that sort of thing). Another possibility is red cabbage, which (unlike cucumbers) is at least starting to be seasonal at the end of October.
What's in season now are root vegetables, squashes, and some greens and cabbages. You'll need something that can stand up to or compliment a rich dish like goulash, how about roasted beets with sour cream, which would tie into the sour cream in the goulash? It's such a simple dish: roast your beets skin-on (or steam them), let them cool enough then peel with your fingers, then cut them up and mix them up with sea salt and a bit of sour cream. Simple, easy, and really tasty.
Alternatively you could make some red or green cabbage, brussel sprouts pan-fried (after partially steaming them) with some slivered almonds, or if you can find them steamed brussel sprout tops (the leaves on the top of the stalk) sliced up with a bit of butter.