Bacher says all four had injuries that were not life-threatening. The two rescued from the mountain were taken to a hospital. None was immediately identified.
Worsening visibility and 40 mph winds kept rescuers from removing the other two climbers late Thursday.
Storms on Mount Rainier are notoriously fierce and obstinate.
"We were lucky to get two off the mountain," the spokesman said.
About 10,000 people attempt to summit the massive volcano each year, with most doing so in the summer. Only a few hundred climb the iconic mountain in the winter.
The Texas climbers were roped together when they fell on Emmons Glacier. The two women at the end of the rope ended up in a crevasse. Rangers who responded to a cell phone call helped them out of the crevasse.
Hall is originally from Patten, Maine, the park spokesman said. The Seattle Times reports Hall had been with Mount Rainier National Park's climbing program for four years.