On cold, wet nights, as many as 15 men, women and children will crowd into a small emergency shelter on the outskirts of Columbia, Md., sleeping on beds, couches and mattresses on the floor, even though the shelter is designed to hold only six.

"Until two years ago, we never had families in our shelter; it was always individuals," said Linda Thomas, who directs Grassroots, a local crisis intervention organization that supervises the Harriet Tubman facility. "Now we are seeing people whose primary problem is not counseling but housing."

Although it has the second-highest per capita income in the state, Howard County, like the rest of the country, is feeling the effects of hard times and federal budget cuts.

The demand for the county's social service programs has increased, but the resources are lacking. Last year, the county's governmental and private nonprofit human service agencies lost more than $1 million because of federal budget cuts.

But, thanks to a new cooperative effort between the county and local businesses, help for the emergency shelter and other social service programs in Howard is on the way. A group of local business, community and government leaders has formed the Howard County Community Partnerships to help rescue the county's endangered human service programs. Supporters of the new program say it is one of the first of its kind in the country.

"We are writing the book here, and I'm hopeful it will be a model for other communities," said Rabbi Martin Siegel, cochairman of the partnership.

The organization was formed late last year, after Howard County provided a $100,000 matching grant and a challenge to the private sector to raise the additional funds by June 30.

Hugh Nichols, Howard County executive, said the funds are available only for fiscal 1983 and must be used to benefit people who have lost job training, food, health care and other support because of federal and state funding cuts.

In only five months of existence, the partnership has raised $60,000 in pledges and services. Contributions have ranged from $10,000 worth of food, clothing and lodging from a local motel and truck stop to refrigerated space in an Ellicott City, Md., building for food storage. The list of 177 contributors includes more than 35 businesses.

"We have received contributions from $100 to $1,200, and not from the typical givers, although we've gotten those, too," said Pat McCuan, head of the partnership's resources committee. The partnership has attracted more than 150 volunteers.

Last month, the county approved the first three projects recommended by the organization. They are:

* The Congregate Nutrition Program for the elderly, which will receive $7,500 and will begin serving 140 meals a week to senior citizens at eight sites throughout the county.

* The Summer Youth Employment Program, which will receive $10,000 for wages for 10 jobs for disadvantaged teen-agers. Michael Hickey, who directs the county's Employment and Training Center, said that last year he had to limit his recruitment program because federal money provided only 88 jobs, compared with 116 the year before.

* A $16,000 grant that will provide insulation and other energy conservation measures for 17 houses, most of them in rural areas.

At a recent meeting, the partnership's board designated Grassroots to administer the large donation to the partnership of food, clothes and temporary lodging, much of which will be used for the shelter program. The board also agreed to ask the county for matching funds to fight evictions, for job-finding programs and for the local chapter of Fish, an organization that provides emergency services.

The board also approved an additional grant for Grassroots, which provides crisis intervention and counseling in addition to the shelter facilities.

Considered an affluent and predominately rural area before Columbia was built 15 years ago, Howard County's population nearly doubled in the past decade, to 118,000 in 1980. Although the county has Maryland's second highest median income, at $30,328 per household, officials say that it has more low-income residents now than 10 years ago.

Unemployment in Howard County is 5.8 percent this year, up from 3.7 percent two years ago. Manus O'Donnell, director of the Citizens Services Department, pointed out that the human service portion of the budget has grown more rapidly over the past few years than the entire county budget. This year, O'Donnell said, the county is spending $4.8 million for human services, an increase of $500,000 over last year.

And unemployment has taken its toll in Howard, as it has elsewhere. Deborah Galinsky, who has been a housing counselor for the county for five years, said she used to get one or two calls a year from homeowners unable to keep up the payments on their houses. Now, she said, the calls are up to one or two a month.

The idea for the partnership to help deal with such problems came from Columbia developer James Rouse, who was a member of President Reagan's Task Force on Private Sector Initiative. Intrigued by the idea, Nichols asked the County Council a year ago to approve a $100,000 matching grant to spur the business community into action. The partnership was formed last November.

All money contributed to the partnership goes to existing public and private agencies, said Jean Weissburg, part-time director. Staffing, supplies and services to run the partnership have been donated by businesses and the Howard County Chamber of Commerce.

Officials of public and private agencies that serve the community say they view the partnership with a combination of hope and caution.

Priscilla Hart, president of the Association of Community Services, which represents service groups in the county and who is a member of the partnership's board of directors, said that one of the main concerns of the agencies is what happens next.

"Unless HCCP continues to fund these programs, is this just a Band-Aid approach?" she asked.

Theoretically, Weissburg said, the partnership formed between businesses and human service agencies should continue as long as it is needed.