OK, so I, V and Y are (1,2,3) in some order.
SNOW is 22...none of these letters can be less than 4 (I-V-Y are 1,2,3) so they must be 4 ,5, 6 and 7 (or SNOW would be more than 22). So SNOW are (4,5,6,7) in some order.
XMAS is 31. We know that S is between 4 and 7, and XMA must each be 8 or higher. So if XMAS is not to exceed 31, XMA must be (8,9,10) and S must be 4. [S=4]
HOLLY is 40. We know that Y is between 1 and 3, and O is between 5 and 7. If HOLLY is not to exceed 40, L must be 11(the lowest available number) and H must be 12. This means that Y is 1 and O is 5. [L=11, H=12, Y=1, O=5]
PRESENT is 81. S is 4 and N must be between 6 and 7, so P, R, E, E, T must be 70 or 71. The lowest possible total is 71, if E is 13 (again, the lowest available number) and PRT are (14,15,16). N must be 6, which means W is 7. [E=13, N=6, W=7]
The lowest available 'slot' is now 17. Over to you...