I have a road bike that have just enough clearance for 700x28c (continental pro4 endurance 28c). Obviously, this is not the best bike for winter conditions, but what are my best options for tackling ice and snow with that bike?
There isn't. Road bikes are not thought to belong on snow.
The limiting factor for most road bikes for tire size is the brake arch. There are no companies I am aware of making studded or snow tires that will fit in a traditional brake arch on a road bike. The closest I have seen are studded ice tires for cyclocross bikes, but these generally start in the 32/35 range.
There is one thing you can try, if you have disc brakes. It works a lot better than one might think. You can put zip ties around your tire and rim if there is enough clearance. The more zip ties the better the traction. Also the heavier duty zip ties the better. When placing them alternate the heads so that they are on both shoulders of the tire.
I have ridden on ice and snow several times with this method and have yet to go down. I wouldn't get to crazy on them and it helps to keep a pocket of ties, but this method works and does not break the bank like a $100+ studded tire will.
If you can lower your tire pressure slightly that will help as well. I have run this method on a 26" MTB tubeless, running 15psi and it never slipped on a parking lot covered in 1" of solid ice, that i had trouble walking on.
What you want is larger tires and possibly studs. You can get studded tires that are 30mm and even then there needs to be room for the studs themselves.
It is possible to do a 650b wheel conversion if your road bike wheels are 700c. The smaller wheels leaves more room for tires. In essence you need to get 650b wheels and tires. If you have rim brakes then you also need to get brakes the have 17mm longer reach so to still have the brake pads go on the rims.
If you have a very narrow road bike then the size of the tire might still be limited by a narrow chainstay or narrow forks so its not a magical solution but it will give more room at the seat tube and brake arches.