As quest items, snowglobes are not removable from your inventory. While playing the DLC, I found it and continued playing as usual. Now, as I check earlier saves, none of them have the globe in the inventory at all, even after I go back to the location and check each time to verify it was actually picked up.
Courtesy of Google and The Vault, "Sierra Madre snowglobe is a miscellaneous item in Fallout: New Vegas. Found in Salida del Sol North. When picked up the player is rewarded with 2000 Sierra Madre chips and the item disappears. "
Sierra Madre, the Snow Globe is located near Dean's Secret Stash in the upper levels of Salida del Sol North. From the southern-most entrance to Salida del Sol South (in Salida del Sol North), proceed down the stairway to the streets and look behind you for the entrance on the floor above. This area can be reached by going up the stairs located to the east and following the rooftops back towards the hole.
"If you don't stand behind our troops, please, feel free to stand in front of them."