This is going to be my first winter beating around on the snow and ice.

What are your opinions on having toe clips?

One side of me says "good idea as it will stop my foot from slipping off frozen pedals." The other side says "it will trap my foot when I slip and want to put my foot down".

I'm really 50-50 on this.

Try Toe Clips without straps.
That is the way I ride all the time.

Half clips.

power grips all the way

Half-clips and toe-clips aren't worth it... without the straps they gain isn't awesome and you can't wear giant warm winter boots with them on your bicycle.

Get a wide platform pedal with aggressive stud grips, this will keep your foot planted for the most part and enable you to dab your foot quickly.

Winter isn't a time to START using clipless. But if you are a regular user of a MTB pedal system that sheds mud fairly well, I see no reason to change for the winter, unless you are using warmer none-cleated footwear.

I run clipless year round. In deep snow it's not preferable, but otherwise it's immaterial.

By toe clips do you mean clips/straps or do you mean SPD style? Clipless (eggbeaters) year round for me.

I'm running with Power Grips and a lightweight (-25 F rated) winter hiking / snowshoeing boot. I have big feet (14) and toe clips don't allow my foot to go in far enough. But even for smaller feet, Power Grips are adjustable to put whatever part of your foot you want on the platform, as opposed to a pre-set placement. For example, with toeclips, a person with a size 11 will be pedaling with a foot more forward than a person with a size 8, which may not be optimal for either person.

I'm takling about clips/straps.

What are power grips?

There are some who use them but I think the general consensus is that they are too big of a pain in the winter. You can't easily get in them with big warm boots. You can't get out of them fast enough when you have an emergency. If you want to use clips in winter it is better to go with MTB style clipless or Powergrips.

Probably the best option for experimenting is an SPD clipless as they have models which are combined with a large platform pedal so you can try the clips or go with regular shoes or boots.

I use clips and straps all the time... my boots are size 9 and smoother at the sides and fit well in wider mtb resin clips. I need this as I ride fixed for most of the winter and foot retention is essential.

Getting out of them in an emergency has never been an issue and my boots will keep my feet toasty and perfectly dry to -30C.

+1 to Powergrips

https://powergrips.mrpbike.com/

I would have been unable to deal with toe clips today. The snow and crap was so thick that I didn't have time to flip over to the platform side of my double sided pedals... I need to work on running mounts or something for the winter cause there were times today where I had to try 5 or 6 times to get started.

Another trouble with toe clips is that you might be wearing pretty thick boots one day and regular shoes another.