Ok, trash and debris on the floor and broken glass wouldn't make a property legally uninhabitable as that is something that could easily be cleaned up. In order for a property to be considered uninhabitable so as to allow a tenant to terminate and move without repercussions there have to be big problems, like sewer backups, electrical outages, no working heat or water.
So the frozen pipes could potentially be grounds to terminate if the landlord didn't take steps to cure the problem when you notified them about the pipes. "Due to how the house is built" is not a logical excuse as the pipes can always be insulated or wrapped in electrical pipe heating tape.
Under IN law (Indiana Code §32-31-8-5, §32-31-8-6) the landlord has to do the following:
Deliver the premises in a safe, clean, and habitable condition
· Comply with all health and housing codes applicable to the rental premises
· Make all reasonable efforts to keep common areas of a rental premises in a clean and proper condition
· Provide and maintain the following items in a premises in good and safe working condition, if provided on the premises at the time the rental agreement is entered into:
o Electrical systems
o Plumbing systems sufficient to accommodate a reasonable supply of hot and cold running water at all times
o Sanitary systems
o Heating, ventilating, and air conditioning systems. A heating system must be sufficient to adequately supply heat at all times.
o Appliances supplied as an inducement to the rental agreement
With that said, if the landlord is violating the above, you can file suit against the landlord for breach of contract and seek damages if you notify them of the problems in writing and they fail to correct within a reasonable time..
Ind. Code § 32-31-8-6
(a) A tenant may bring an action in a court with jurisdiction to enforce an obligation of a landlord under this chapter.
(b) A tenant may not bring an action under this chapter unless the following conditions are met:
(1) The tenant gives the landlord notice of the landlord's noncompliance with a provision of this chapter.
(2) The landlord has been given a reasonable amount of time to make repairs or provide a remedy of the condition described in the tenant's notice. The tenant may not prevent the landlord from having access to the rental premises to make repairs or provide a remedy to the condition described in the tenant's notice.
(3) The landlord fails or refuses to repair or remedy the condition described in the tenant's notice.
(c) This section may not be construed to limit a tenant's rights under IC 32-31-3, IC 32-31-5, or IC 32-31-6.
(d) If the tenant is the prevailing party in an action under this section, the tenant may obtain any of the following, if appropriate under the circumstances:
(1) Recovery of the following:
(A) Actual damages and consequential damages.
(B) Attorney's fees and court costs.
(2) Injunctive relief.
(3) Any other remedy appropriate under the circumstances.
(e) A landlord's liability for damages under subsection (d) begins when:
(1) the landlord has notice or actual knowledge of noncompliance; and
(2) the landlord has:
(A) refused to remedy the noncompliance; or
(B) failed to remedy the noncompliance within a reasonable amount of time following the notice or actual knowledge;
whichever occurs first
So based on your comments, it doesn't appear as though you would currently have legal grounds to terminate the lease without potential repercussions..