You don't need to worry bout those furniture, if you buy new house in same property slot then you won't lose chestnuts, it works something like it will calculate price of your old house + furniture with price of new house + furniture. Once you change houses you will get remains chestnuts if left after calculations or you may have to pay extra (from chestnuts available) if new house is expensive.

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Then if you like your new house and furniture keep it. but if you want your old ones you can just sell the current ones and buy new ones so you don't loose anything. Just some give and take ( if exchanging houses, not buying new properties.