A four-season porch is an addition
Call it what it is: a heated, insulated room built to the same envelope standards as the rest of your house. Footings or foundation work, framed and insulated walls, residential windows, ductwork or its own heat source, permits, and a construction timeline measured in months. Done well it is wonderful. It is also, functionally, a home addition with a lot of glass in it, priced like one.
A three-season porch is a shelter upgrade
A three-season room is unheated. Its job is to stop wind, rain, snow, and bugs while keeping the outdoor feel, and the modern version of it is frameless retractable glass fitted to a porch, patio, or deck you already own. No foundation work, no insulation, no furnace tie-in. Install is days, not months.
The name undersells it in practice. An unheated glass room in Minnesota is comfortable far past what "three seasons" suggests, because glass kills windchill and traps solar gain. A sunny 40-degree afternoon in February is porch weather behind glass. What it will not do is hold 68 degrees on a January night, and anyone who tells you otherwise is selling something.
How to choose in one question
Will you use the room on winter evenings, or do you mostly want your porch season to stop being four months long? If it is the first, budget for the addition. If it is the second, and for most families it is the second, retractable glass gets you there for a fraction of the cost and disruption, and unlike a four-season room it opens completely in July.
There is also a sequencing argument: plenty of homeowners glaze the porch now, live with it for a few years, and discover they never missed the furnace.
Wondering which your porch calls for? An hour with a tape measure settles it, free.