Is it customary for a host of a dinner party to pay for the cost of food in this country?!

first what country?
In the USA if you throw a party its your cost unless you say its "pot luck" or bring a "covered dish". Its usually reciprocated then by your guests inviting you over to their homes.
I do not know what you mean by "hot pot", but it sounds like youre cooking one big main dish.
If anyone asks to bring something, its ok to say yes, like a bottle of wine or something like that. The only time you can split cost is with your family or if a group of friends got together and they all decided to chip in, but not after you have invited them.

I would assume from some of the answers that your suggestion is acceptable in the USA. I live in France so I asked my neighbour Claudine if she would ever ask anyone to bring food to one of her dinner parties or ask for money to pay for it. She thought it immensely funny and that I was making the English joke, so I showed her your question (translated ) and she was aghast. She said that if she ever said anything like that to her friends she would be ostracized and would have to leave the district. She asked me in low tones "You have been to America, are they all slow witted?" So there is your answer from across the pond, it is definitely a faux pas of major proportions.

Yeah, that's a touchy subject. Like someone said, you definitely would want to ask everyone a few days or whatnot before the party - definitely not during or after. Something that my family always does is have each guest bring a dish. One person is asked to bring dessert, another person is asked to bring a vegetable, another person brings bread, and so on. In TX, we call it "pot luck" style.

if you are in the US, you can ask them to bring a dish to pass around. usually though the host pays for everything at the party

i have lived here my whole life, and go to parties regularly

rude? yes, slightly. especially if you tell everyone to pay AFTER the party.
But if you ask everyone before-hand and they all agree, then it's alright.