Now I’ve taken the delightful Christmas trimmings down from the site, I thought I should let Richard put you out of your misery (or just confirm what you had already cleverly worked out for yourselves?).
Christmas Puzzle 1
White to play and win.
It does appear impossible to prevent the pawn on a3 advancing
Christmas Puzzle 2
White to play and win.
Christmas Puzzle 3
White to play and draw.
Christmas Puzzle 4
White to play and draw.