All good advice, regardless of where you live and fish.
Specifically in regards to the initial question, rain and snow together WILL add weight on top of the ice.
If the ice was thick enough before the rain/snow fell, it should be fine...messy but fine.
It is always smart to check more frequently under these conditions to see if there are any drain holes or spring holes under the slop.
Both of these will erode the ice without giving clear indication on the weakness until added weight is applied (you, a sled, an ATV...)
If the water cannot drain off it will aid in melting because it will absorb heat from the surrounding air and radiant sunlight.
Hopefully the conditions improved after the rain/snow fell, allowing for more "safe" fishing trips...