I’m assuming you’re in the US, look up the prices for vinyl fence on home Depot or Lowe’s website. They have pre build items for that type of fence. I would 2-2.5x your material estimate to account for labor, markup, and misc items that are needed. Removal and haul away of a chain link depends on what it looks like now. All in I would guess $4-5k if there isn’t much custom work.
I would say that if you are physically capable and have the time, fences are pretty easy to DIY with a shovel, level, and drill. there are plenty of resources online showing you how. And make sure to call your local dig safe number.
Have you looked at microspikes? They go over any shoe and give you way more traction on snow/ice. Hiking boots will still slip on ice.