To tell you the truth, I dont know.
I have to admit, I personally would feel better having it on there during winter. Since the dealer misplaced it, it makes sense to me that they replace it, their cost. No matter if you need it or not.
The fact is, they lost your property, so they should pay for the replacement. Just have them get you a new one and you'll have piece of mind. That's what counts.
Best of luck and happy holiday!
81 300 SD grey/palomino 168K miles
84 190E 2.3 black/grey 64K miles (wrecked)
85 190E 2.3 maroon/palomino 92K miles
88 300E desert red/palomino 204k miles
(made to look like a '94-95)
92 400E desert taupe/creme beige 120K miles
(converted to 94-95 E420 looks)