[Edited 2 Jan to add a hint of uncertainty to the identifications]
Over the holidays I was able to spend a few days at my parents' house in upstate New York, and enjoyed the redpolls that were visiting the bird feeder. I saw one clear-cut Hoary and at least two other Hoary-type Redpolls, and at least one "Greater" Common Redpoll among the flocks of regular Commons. There were up to about 60 redpolls at once visiting the feeder, but there must have been far more that passed through during the biggest day (29 Dec) since the unusual redpolls were each only seen for brief periods. I set up my Wingscapes Birdcam and just let it run, and ended up with a pretty good assortment of redpoll pictures, including a couple of Hoaries that I didn't see in real life.
I saw one really pale Hoary that stood out as a very white bird. Unfortunately that one didn't get caught by the birdcam. I did get pictures of several of the more subtle Hoary-types (clicking an any picture below will bring up a higher resolution image that shows more detail).
Here's a typical scene under the feeder:
Notice the brownish backs of the Commons, and the one paler bird towards the right is an adult male (pink showing on the breast) so it's just a Common. Below is a shot from a few minutes later, and there on the left is a paler bird - a female Hoary-type!
Notice the grayish back without the brown scapulars of the Commons, the clean white facial markings and pale neck. But it's certainly not "obvious". Below is the same bird moments later next to a Common:
Again, compare the ground color of the sides of the back (and scapulars). Commons typically have two white stripes down the center of the back, contrasting with brown stripes towards the sides. On Hoary the back is more uniform - white in the center and pale gray on the sides. Towards the rear, where the rear scapulars overlap the wing coverts and tertials, Hoaries have the scapulars edged whitish so the rear edges of the back are paler, where the same feathers on Common are just brown. The pale edges of wing and tail feathers are whiter and broader, the supercilium is unstreaked white, and the sides of the neck are pale and faintly streaked.
Below is another Hoary-type (more subtle) with its back to the camera:
And a Common in similar pose below:
Notice the difference in back color and pattern. The pattern and extent of wing markings is similar (and extremely variable) in both species, but Hoaries often look whiter there. And below is the same Hoary-type with its head up:
Notice the short, stubby bill, pale neck sides, "frosty" back and wings. Below is a rather large-billed Common to compare, but bill size is not always different:
Finally, below is an ambiguous individual:
This bird is heavily-streaked below and on the neck-sides, a bit brownish on the back, etc, and I doubt that anyone would call it anything other than a Common, but it's paler and grayer above than a typical Common, and could be intermediate. [One might say this is on the Common side of intermediate, while the Hoary-type above is on the Hoary side of intermediate. Both may be unidentifiable, or at least many people would want to see a less ambiguous individual before making the call.]
After this experience I suggest that back color is one of the best things to look for as a first-cut. Then try neck-side markings, bill size, streaking on flanks and undertail coverts, and then other features. The paler color of Hoary is expressed as an overall whiteness and "clean" or "frosty" appearance. For example, on birds with a buffy wash on the face and throat this leads to a cleaner yellow-buff color, which on Commons is sullied by thin streaks and dusky smudges. All features overlap between the two species, and it's difficult to find anything objective to latch onto and to support an identification. Therefore it will be difficult to identify the more subtle Hoary Redpolls unless you get a really good look at the whole bird and have looked carefully at many other redpolls, but there is definitely a clean, pale overall appearance that is associated with Hoary.