you could glue candy canes to the side
cut out snowflakes from construction paper, or buy glittery snowflakes and glue those to the side.
red and gold ribbons and bells
guessing you mean straight cotton-line it with Christmas towels or colorful linen napkins.
or maybe holiday tissue paper.
Instead of a basket, buy a little stocking, and fill it with tinsel and candy canes, and all that kind of stuff. I personally love stockings, so that’s what I’d want somebody to get me. It’s a creative, fun and festive gift.