Police suspect that Williams may have fallen while getting out of her auto when the two returned home, and Haley tripped over a rug on her way to phone for help.
Temperatures fell into the single-digits overnight Saturday due to Arctic air filtering south from Canada.
Investigators say Ms Williams lost her footing first and Ms Haley fell as she tried to go for help. Jean is thought to have fallen in her garage, while Martha may have collapsed in the driveway heading for her auto.
According to police, the women spent hours outside in the cold before succumbing to hypothermia. Haley was found in the garage.
The twins had just returned on Friday night to Ms Haley's home from dinner with their 89-year-old sister. They were rushed to Rhode Island Hospital in Providence in critical condition, but died shortly after. A cause of death has not officially been determined, but authorities said in a statement the "extreme cold temperatures that evening may have been a factor". Relatives outside the isolated waterfront home said they were still in too much shock to speak to reporters on Sunday, the Providence Journal reports.
"They came into life together and they died together", John Haley, one of Jean Haley's sons, told TIME on Monday.