Sadly, they will accumulate a lot of snow and ice in my experience that last time it snowed a few weeks ago - and I'll admit I have posted to the contrary before. My commute was only 6 miles with no highways fortunately, but when I got home there was a good half inch of crud packed into the lights and I could tell while driving that they were impaired in some way.
In all other situations, I believe the JWs are better. I have run both on my Jeep - the Wife has the TLs (non-heated) now and she likes them well enough.
So yeah, the snow problem is real. I know you're safety minded with the kids and all. I would recommend you take a hard look at the Heated TLs. D-nought has them and could vouch for their snow performance.