I recently read an article, myself wondering what is the majic number - of how many inches of snow makes an inch of rain? It seems it depends on the snow characteristics. And there's many different types. It's hard to call it, but, a general figure of approx 8" of snow = an inch of rain.
Slow melting snow beats a hard downpour, for replenishing the underground supply.

Well, snow melts SLOWLY and seeps into the ground ... it's actually better than rain because more of it goes into the soil for the plants.

And how much snow = 1 inch of rain varies with the "wetness" of the snow. They not only measure the snowpack but melt it down to see how much water is in it.

I know this is an old post...but...in far north winters, the snow melts before the ground thaws, so much of that precious water is lost to "runoff". I would think a driving rain would be more beneficial.

Where I live in the high desert you want either rain or a good slushy wet snow. If the snow is dry, the moment our intense sun comes out the snow mostly just evaporates with little getting into the soil except in shady spots.

That's a tough question. I would go for snow. Here in the mountains of Colorado, the snowpack is the reservoir for much of the West. The melting snow keeps rivers flowing, and the effects of minimal snow are less-than-fond memories last year and infamous instances such as the no-snow winter of 1976 (or was it '75 or '77?).

The trick with rain (as with snow for that matter) is timing. A couple of recent experiences...

First, about five years ago, it rained almost every dang day from late June to early Sept. There were mudslides galore, but there was also lush growth everywhere. However, it was soggy -- a condition hardly ever seen here in the high Southwest, along with stuff like mold and other humidity/moisture/mildew issues that Eastern gardeners battle on a daily basis. Too much growth and lack of bright sunny days (cooler than normal weather) prevented berries from growing, and a previous June frost stunted or killed the scrub-oak acrons. The bears were starving in autumn, and scores of them began foraging in in-town garbage cans, even breaking into kitchens. For several weeks, the bears seemed to be everywhere. That was too much rain. Everyone pretty much stayed indoors all summer, no camping, no hiking, no biking (yes, we were wimps!), and the mosquitos were particularly nasty.

The second instance was an exceptionally rainy April and May followed by the usual bone-dry summer. The early rains spurred all kinds of tender new growth on shurbs, grasses and trees. The plants were totally psyched on all the moisture right at the start of the growing season. They went nuts. The problem was, when the rains stopped, there was nothing to support and maintain all this new growth. Tall grasses dried quickly. Shurbs became tinderboxes. The dry storms (lots of lightning / little rain) ignited tons of wildfires that year.

To add my opinion for the question, "would a lot of snow then no rain equal a lot of rain then no snow?" I'd say no. There are different implications for each extreme. While both have drought results, from my experience, it's much worse to have no snow. The rains soak into the soil and don't fill up the reservoirs and man-made lakes that we depend on for domestic water. The melting snow in the high country (10,000+ feet high) provide the water for our streams and rivers, too. My vote goes for snow being the most important. But it's a real Hobson's Choice if you have to pick winter snow only or summer rain only. FWIW.

In ND rain is alot better then snow for moisture. The ground is froze so hard that when the snow melts alot of the moisture just runs off instead of soaking in. Julene

Here, snow/rainrall can vary from 1:6 (very, very wet snow) up to 1:12 (very dry snow). Just depends on the time of the year with dry snows ususaly (but now always) coming early in the winter and wet snows coming later (March, April, May).
I'll take snow for ground recharge spring runoff-Driving rain doesn't do much except help flodding and mud/rockslides. Also, many natives here are well adapted to the meagar rain events we get and are effecient water users in that respect. Good wet, late winter snows that slowly melt into the ground will do more for most plants here than an couple of inches of rain in one short duration event.

in the southwest they always say snow is more needed then rain for our ongoing drought.