The Conundrum will fit a 3.8"/4", but will only fit a larger tire (Big Fat Larry) if you modify the crown of the frame. A studded tire will further reduce crown clearance, so it’s possible that you’ll have to modify the Conundrum frame with a studded tire.
There is no such thing as a 4" tire for a 24" wheel, Surly made the Large Marge rim in a 24", but never made a tire to match.
Your best bet is an Oregon frame, it will also be the least expensive option at $160 USD. The Oregon will all fat tires currently in production.
Also, just a thought before you go and buy a fat tire, the 4.5-5" tires are an overkill for a muni and tend to worsen some of the fat tire characteristics that make riding a fat tired muni a challenge.
In other words, get a 3.8"/4" studded tire or a standard 3.8"/4" tire without studs.
Studs are only helpful for ice, studs will no help you in mud and snow.