How much does a few months of exposure to snow and rain affect lumber?

Left unpainted, your porch would probably last decades (assuming there's a roof over it). We often see this in barns, sheds, and people who want a "weathered" look for siding. Along the way, the wood will stain, gray, and lose it's smooth texture.....but that takes years. Make a visit to your lumber yard and you'll see framing lumber stored in open air stalls with only a roof. Standing water is more of a concern, but if built correctly, your porch shouldn't have any.

In your case, a few months of exposure is nothing to worry about. Before you paint. you'll want to kill the mold so it doesn't bleed through. Probably a mix of chlorox and water would do the trick. Don't paint at the crack of spring. Wait until the sun has had time to dry the wood thoroughly. If you opt to cover the porch with a tarp or plastic, be sure to allow good air-flow. Plastic can hold moisture in as well as keeping it out.

Untreated, it can mess it up, as others have already pointed to. Covering the area with a tarp if you are in someplace with a real winter, is the best option. The tarp/plastic should not be in direct contact either, secured like a roof and done for the snow and wind loads that may be hitting them.

the next time the weather is warm enough, kill off the mold with 1:10 bleach solution.

Let it dry, and then apply paint or sealant. It may warp from the moisture if you let it, but tarping it won't make things better, but could make things worse. Moisture will still get to it, even if it's covered.

Rain/melted snow can make untreated wood swell, warp, crack and cause mold growth,

yes, cover with plastic or a tarp to protect it, don't seal the plastic around the porch, it needs air flow, it's just to keep rain/snow from sitting on the wood.

Mix 1 part bleach to 9 parts water and wipe down to kill the mold.

Not good. Only time will tell. Get the wood treated and painted immediately when weather permits.