Oh my goodness!! You will get mom of the year award from her and all her friends. (Not that,that it is what you are looking for. Just pointing out how special this is)
You both will have such a wonderful time making memories that will last forever in her heart.
I am another vote for buying the tickets. Take the Amtrak and stay in a nice,yet inexpensive hotel, find a couple very "Chicago" type restaurants to dine at. Check out groupon.com for dealios.
Make the tickets into a package deal kind of gift for her to unwrap on her magical, Christmas morning . Put her ticket in a beautifully decorated box, find a masquerade mask and a make a nice itinerary typed up of where you will stay, where you will eat and how you are getting there. Oh my...she will go berserk with excitement!! Or...just go with the tickets...I can sometimes go overboard in my head with planning when I am not footing the bill :)
Again...I say go for it!! Don't let weather hold you back. But then again..that is the California girl in me talking. I have absolutely NO CLUE what real harsh weather is like.
Sooooo, if you end up doing this..you have got to come back to MP to tell us how she reacted and how your adventure went!!!!!