As freezing weather descended this week, Richmond faced the biggest test yet of its new cold-weather shelter system — one based on using hotel rooms rather than a city building as the overflow space after existing shelters are filled.

How well the system worked under the guidance of a coalition of nonprofits known as the Greater Richmond Continuum of Care and backed by the city with millions of dollars in federal funds has yet to be determined.

The city, Homeward and GRCOC have not issued any data on the number of homeless people accommodated.

But concern about the adequacy of the new system and its narrow focus on cold weather to the exclusion of other severe weather conditions, such as the heavy rain that hit the city last week, is leading one City Council member to push for creation of a year-round city shelter that could serve people in need during periods of high heat and heavy rainfall, as well as when temperatures fall below 40 degrees at night.

Councilwoman Kristen N. Larson, 4th District, chair of the council’s Education and Human Services Committee, has introduced a resolution earlier this month requesting that Lenora Reid, the city’s interim chief administrative officer, present a report “identifying a location for an inclement weather shelter.”

The shelter would operate when the outdoor or wind chill temperature falls to 40 or below as was the case Monday, Tuesday and Wednesday of this week, but also when the outdoor temperature is 92 degrees or hotter or when the forecast calls for an inch of rain, a tropical storm, a tornado or high winds, according to the resolution.

Ms. Larson plans to take up the resolution at the Thursday, Dec. 3, meeting of her committee.

Creation of an all-weather shelter has been a top priority for homeless advocates and would be a first for the city, which has largely limited shelter service to winters, although it has opened daytime cooling space offering water and air-conditioning during the hottest summer days.

Ms. Larson’s idea picks up from a unsuccessful effort of outgoing 2nd District Councilwoman Kim B. Gray, who had pressed since the summer for the reopening of the Annie Giles Community Resource Center as a shelter and urged that it serve people during all inclement weather.

While Ms. Gray failed to win council backing, Ms. Larson’s resolution offers the city an opportunity to find other space to offer an expanded operation.

There is no published data on the current need. The last report published in May on Homeward’s website indicated that the GRCOC coalition was accommodating 368 people during one week in existing shelters and in hotels that were brought online after pandemic funding provided accommodations for the homeless.

One report, though unsupported by documentation from Homeward, indicated that 120 people were accommodated in hotels in October when the temperature on one night dipped below 40.

Under the current system, the main link to shelter is the Homeless Crisis Line, (804) 972-0813, which often takes messages that are returned later.

But not everyone knows to call.

“There were some still sleeping outdoors unaware” of how to connect to the new shelter system, said Rhonda Sneed, a founder and director of the volunteer group Blessing Warriors RVA that has been on the front lines of providing food, clothing and other aid to the homeless.

In a Facebook post on Tuesday, Ms. Sneed noted that she learned for the first time that Homeward had contracted with the nonprofit transportation provider Go to Work RVA, (804) 548-4310, to provide homeless people free rides to the hotels when they were approved for a room.

She also stated that different people involved in the shelter operation offered different information. For example, she stated she was told at a hotel that people could just show up, but then was informed by another person that those seeking to check in “must first go through the crisis line.”

Ms. Sneed also stated some people who called the crisis line were turned away because they asked for a hotel room and did not say safety net. The crisis line also closed at 9 p.m., so homeless people later found outdoors could not connect, she noted.

Ms. Sneed reported that “a young lady was turned away and had to sleep in her car” Monday night, when the temperature fell to 39 degrees.

The Free Press confirmed Wednesday that there is a shortage of beds in a call to the Homeless Crisis Line. The responding operator reported that all hotel rooms designated for the “safety net shelter” were taken and that no information was available on whether additional space would be provided.

“There are still people out there, but I have no idea where to direct them,” Ms. Sneed said. “No one knows what to do.”