You don't need or rather shouldn't use this option if you actually intend to be with Ophelia, you can easily get that horse without it.
You need to grow them yourself, as there is no shop that sells vegetables. Once you started to work on the field for Penny and her affection is high enough you can also ask her for a few vegetables as a present to you.
Oh and "Vegetables" were removed in the Penny Update and replaced with "Carrots" and "Cabbages" (the Carrot would be required for the horse)
I don't know how to help you if you couldn't find the hut itself with the help of the walkthrough and the in game dialogues, as Rick already gives you a very detailed explanation where to find it... in what map are you stuck exactly?