Once the heating problem is documented, the owner has a right to be notified and needs to be given a reasonable amount of time to fix the problem.
If all of that has occured, then there is a potential for you to get out of the rest of the rental period and sue for the remaining prepaid rent. Also, if the house was uninhabitable during the winter while you paid rent for it, then you may be able to obtain a retroactive rent abatement for that time period. The retroactive rent would be the difference in value between the apartment with the heating problem and what you actually paid for it. (Ie. if your rent was $1000/month but the apartment is only worth $500 with the heating problem, you would be entitled to $500/month for those months where the house was uninhabitable).
The basic option at this point is to sue or ask the landlord to submit to arbitration. If the total amount of your damages is less than $5000, you could bring a case in small claims court.
Otherwise, talking to the landlord to get the issue resolved would be a good idea. It is always best to try to come to an agreement before going to Court.
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DISCLAIMER - This answer is not legal advice. No attorney-client relationship is formed. The information provided is for educational purposes only. For specific advice regarding your situation, please consult a qualified attorney in your area.