First Lady Nancy Reagan offered some Christmas cheer to kids at Children's Hospital yesterday and got hugs and crayon-written notes in return.

"I watch you on TV sometimes," one little girl told Mrs. Reagan. "I hope you have a better year next year," another said.

The first lady has said in several interviews that 1987 has been an especially hard year for her. She underwent surgery for breast cancer, her mother died and her husband was weakened politically by the Iran-contra affair.

Mrs. Reagan, wearing a red knit dress, was making her sixth Christmas-time visit to the hospital in Northwest Washington. As in previous years, she presented a check -- this one for $25,000 -- to the hospital to buy equipment.

The money, to be used for dental X-ray equipment, was donated by NBC-TV, the American Telephone & Telegraph Co., the Revlon Group and U.S. Fidelity & Guaranty Insurance.

Mrs. Reagan's visit began with a brief ceremony in the lobby of the hospital. She was greeted by children gathered on the steps of a carpeted platform and by Christmas carols sung by the Maryland Boys Choir of Silver Spring.

Two little girls who have been treated at the hospital -- 2 1/2-year-old Emilee Dobish of Virginia and Salinda Smith of Georgia -- held each of Mrs. Reagan's hands and escorted her to the microphones.

"I hope with the new year that all you children will feel better, will have good health and happiness," the first lady said. She then began making the rounds of rooms on the fourth floor of the hospital, delivering toys to each child along with a few words of encouragement.