You definitely want a second set of wheels. If your "primary" set are alloys, I assume you might actually care about them, and you don't want the guys at the tire shop mounting/dismounting tires and prying off weights twice a year.
That being said, I have a set of alloys for the winter but I kind of "lucked" into them. They were take-offs from a similar vehicle so they are factory wheels but I got a good deal.
We use a lot of salt in my area and to those that say they'll corrode away to nothing - wrong. Yes, there's some corrosion but these wheels have been through 10 winters and they aren't that bad. I don't know how someone is replacing 2 alloys a year - crazy. Maybe they need parking lessons or are trying to run too low a profile on bad roads in the area. Or maybe they need to spend more money on a quality wheel instead of throwing two away every year.
To those commenting on leaks. Yes, it's generally said that alloys can lose more air than steels but it's never been an issue for me. I have to add air for leak loss very rarely, I'm usually only adjusting for seasonal temperature swings. If your tire shop did not properly prepare the bead sealing area of your wheels before mounting tires you'll have issues regardless of steel or alloy. If there's a little bit of corrosion it needs to be cleaned off. Aluminum corrosion doesn't stand out as much as orange rust and a lot of techs don't bother. Then people generalize on the Internet saying aluminum leaks more.
If you'd like alloys look around and be creative. There are a lot more options than simply walking to a dealer parts counter and saying "how much?" See if they have packages around, look in classifieds/ebay for take-offs. Or run your factory alloys in the winter and upgrade your summers as someone suggested. If you buy alloys, buy quality and they'll be less likely to fail - both the casting and the coatings.
That being said, steelies are certainly more economical and do just fine, assuming you don't have vehicle weight or high torque concerns. If you're a "driver" you will ABSOLUTELY notice the increase in unsprung mass from steelies. On a previous car I used alloys summer and steelies winter and I noticed the extra weight affecting the suspension immediately. To be blunt, if your car is an appliance to you like your washing machine you may not notice or care.