What's your question? Ask

When you say the winter kill damage was extensive do you mean that the damage extends beyond the foliage (for example - is the bark splitting?) And are only the tips of the boxwood impacted - winter burn commonly just yellows the tips of boxwoods but can be deeper and take over a whole bush in more severe cases.

The best thing you can do to help your boxwoods recover is to prune the dead and damaged parts of the plant. You can cut back the tips of the damaged branches to just above a green living leaf. - it is okay to do major trimming in the early spring once the threat of extreme cold snaps has passed and before the boxwoods sprout new growth.

For more information on how to protect your boxwood from future winter injury, please read the following link:
https://www.gardeningknowhow.com/ornamental/shrubs/boxwood/boxwood-winter-protection.htm

For more information on pruning boxwoods, please visit the following link:
https://www.gardeningknowhow.com/ornamental/shrubs/boxwood/trimming-boxwood-bushes.htm

Here is a link that will help.
https://www.gardeningknowhow.com/ornamental/shrubs/boxwood/fertilizing-boxwoods.htm

I would recommend that your boxwood shrubs undergo what is called a "renewal pruning" which is a multi-year pruning process which involves pruning it back in stages. Renewal pruning is described in detail here: https://extension.psu.edu/plants/green-industry/news/2012/hacking-whacking-dealing-with-overgrown-shrubs

For more information on the care of boxwoods, please visit the following links:
https://www.gardeningknowhow.com/ornamental/shrubs/boxwood/boxwood-care.htm
https://www.gardeningknowhow.com/ornamental/shrubs/boxwood/trimming-boxwood-bushes.htm

I would say what you are seeing is normal for a boxwood exposed to hot afternoon sun. And, your shrub still looks healthy - I see no yellowing or browning or any sign that it is too distressed.

For more information on boxwood trees, please visit the following link:
https://www.gardeningknowhow.com/ornamental/shrubs/boxwood/boxwood-care.htm

You have a beautiful stand of Boxwood!
Yes, I do think your hedge has suffered some winter damage.
I would allow the plants to recover with adequate water.

Here are some great links to help you with recovery and proper pruning.

https://www.gardeningknowhow.com/ornamental/shrubs/boxwood/boxwood-care.htm
https://www.gardeningknowhow.com/ornamental/shrubs/boxwood/trimming-boxwood-bushes.htm
https://www.gardeningknowhow.com/ornamental/shrubs/boxwood/yellow-or-brown-boxwoods.htm

Your Boxwoods look beautiful!

I really would suggest trying to remove the weeds by hand. Reaching the weeds from along the soil line and making sure the entire weed is removed.
Boxwoods are an investment and to risk harming them with a weed killer may be very risky. Once the weeds have been removed I would mulch around the base of the plants to inhibit regrowth of weeds.

I have listed a link that may help. Perhaps using the cornmeal would inhibit the weeds from seeding again.
It may be worth a try.

https://www.gardeningknowhow.com/special/organic/cornmeal-in-the-garden.htm