It is very important to be clear and clean when requesting refunds and compensation from Lufthansa. Using terms like 'downgrade' may delay the correct processing. Irrespective, the refund should not take that long.

Sounds unfortunate, but you were not downgraded. A downgrade occurs when you present yourself for boarding and you are given a seat in a lower service class - a missed connection is not a downgrade. While LH will reaccommodate you in the upgraded class of service, it requires 'availability' and I assume that just wasn't the case for the flight next say.

Given that the misconnect was due to weather, there shouldn't be any EC reg 261 compensation due and it sounds like you got a taxi and hotel in the end. The easiest at this point is likely a 'credit card charge-back' for the upgrade fee. 'Services were paid, but not delivered' - most CC issuers will view this as an easy case and you should have your money back in a few days.