I don't walk much in deep winter snow, but I often am forced to walk through spring slush. I have tried several lightweight solutions.
1. Sealskinz socks with a waterproof membrane and fleece lining. These work well with running shoes or boots, but will eventually spring a leak due to the big toe wearing a hole in the membrane or the seams pulling apart. Once there is a leak, these socks provide little warmth, because fleece is not warm when wet. Theses socks aare fairly inexpensive and lightweight, so the obvious solution is to just carry two or more pairs on a long journey.
2. Non-breathable neoprene socks. These socks are very warm and remain warm even after springing a leak. However, they are generally too warm in conditions where slush alternates with dry ground, so that the foot gets soaked in its own perspiration.
3. Breathable neoprene socks. These socks are made by seirus.com and used to be sold by campmor, but no longer, apparently. There are two layers of nylon jersy, with neoprene sandwiched in between, and with tiny holes in the neoprene. Perspiration wicks along the inner nylon jersey shell, then evaporates through the holes. Of course, exterior moisture can also get in through these holes. However, neoprene is warm when wet, so this is not usually a major problem. These breathable neoprene socks can be worn with either shoes or sandals. With sandals, the neoprene will soon develop tears. But again, since neoprene is warm when wet, this is not that big a problem. This is my current slush solution for use with sandals.
4. Neoprene booties. These can be worn alone, since they have a fairly durable sole. So you could carry both neoprene booties for slush plus some lightweight running shoes or sandals for dry ground. I haven't yet tried this solution, so I don't how durable these booties are in practice. But they aren't that expensive, and neoprene is warm when wet, so you could just bring these along for the first few weeks of a long journey, then throw them away after all the slush had melted.