I don't know those two different makes of tires, but this much I can say - the second set looks more worn to me than it might appear. When you're dealing with winter tires, keep in mind that tread life is not 10/32" (100%) to 2/32" (0%), it's more like 11/32" (100%) to 5-6/32" (0%). Unlike normal tires which will function in the dry just fine with very low tread depth, snow tires absolutely will not function in the snow/ice without a pretty significant amount of it.
The tires you've shown pics of in your post look to me to be at around 5-6/32" tread depth, so they're probably getting reasonably close to their end of life. Will they last one season? Probably, but they certainly won't be ideal for that season.
I can understand wanting to just save the money and get rid of the car next year, but consider another option that may save you in the long run - buy a lightly used *set* of winter wheels/tires now, and sell them next year. This does a couple things for you - reasonably priced winter sets are usually pretty easy to sell (I would imagine even easier in your area). If you get one used now, you've let the first owner take the depreciation hit, and you will likely end up losing only a couple hundred dollars. Also keep in mind that most decent tire shops will charge you from $70-100 to swap a set of tires, and you'll have to do this twice if you put winters on your current rims, then again in the spring to turn in your lease (unless BMW will accept the car with snow tires on it?). Those are sunk costs, and the whole process takes more of your time, not even to mention the cost of the used snow tires.
I don't know if I've been helpful here, but it's just food for thought. If you're still not convinced this is the way to go for you, I'd probably go with option 1 in your list. At least you could probably sell a near-new tire that you buy now after the season is over. With the second set, as I said, they look close to shot already, so it's extremely doubtful they'd be worth anything at all. Not to mention you'd get a safer set of tires with the first option since they're newer.
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