Reddit mentions of Fleece Ear Warmer

Wool is good for Autumn, down-filled puffers are good for winter. I would reconsider your budget and maybe go for a fall ensemble first and save for a winter outfit. I think both of your coat choices are good, by the way, just not both for winter :)

Some things to consider:

• Getting a good pair of rain boots will not only help on rainy days, but you can also buy liners (like these) for wintertime. Rubber rain boots will hold up better than most other winter boots, especially when you start to get the slush and wet snow.
  
  
• As /u/peanutbutter_banana mentioned, the wind is killer here; invest in good, thick winter accessories. You'll need scarves, hats/earmuffs (this style wraps around the back of your head, which allows you to still wear a hat comfortably), and waterproof gloves. If you have a smartphone, get tech-friendly gloves so you can use the screen without having to freeze your fingers off.
  
  
• Socks: get some good quality wool socks. Wool will help wick moisture away and insulates better than cotton (this is actually an all-weather tip - thick wool for winter, thin for warmer weather)
  
  Source: I live right off the lake. I just moved back to Chicago after living in Arizona for 5 years, so I feel your pain!
  
  ^^^^Edit: ^^^^Added ^^^^link