When to prune?
About half the cedar is brown and brittle. Should I cut this all off?
Where is the best exposure for these trees. I live south east of Edmonton, Alberta.
If you have ruled out disease, it is likely that winter damage has caused the die-off of parts of your globe cedar, which although hardy, is still susceptible to extreme winter conditions. As far as exposure goes, a local nursery may be able to provide you with advice that is targeted to the Edmonton climate. Edmonton is Zone 3b and Toronto Zone 6, so it is hard for us to provide specific advice here. Landscape Ontario has a guide to protecting evergreens for the winter, including advice for globe cedars, which are prone to snow damage: https://landscapeontario.com/winter-protection-for-delicate-plants.
Spring is generally considered the best time to prune cedars. Here is a previous Toronto Master Gardener post on pruning globe cedars with good advice on care as well:
Very best of luck with your cedars.