There is probably not much specific out there on this period because it is not one that seems to get many reenactors or costumers, who are the market for highly specific information about dress and hairstyles in particular periods. A lot of people are into the simple Regency, which requires little in the way of underpinnings, and a lot of people are into the crinoline and bustle periods, which begin in 1856 with the patent for the cage crinoline (or "skeleton skirt", as they're called in several patent applications).

By this point, men's shirts were no longer being constructed of simple geometric shapes; it was becoming less expected that they would be made at home, and the new styles, such as the "corazza" and the "eureka", would have pleated, buttoning yokes set into a full body in front. On top of that, they would wear a waistcoat. If for nicer dress, it would be fairly low-cut and with a shawl collar, in a dull or rich (but not bright) color. If being more casual, the shirt would be largely covered - the correspondence between the amount of white shirt prominently on display and the level of formality would remain for the rest of the century. The coat and trousers would also be fairly basic colors, most frequently black, although very fancy, flashy gentlemen might wear brighter colors and even plaids. Hair was parted on the side and fashionably waved, with a mustache and/or beard.

As noted above, women were not yet wearing hoop skirts. Instead, their gowns were held out by wearing several starched petticoats, often with extra-stiff petticoats made out of linen and horsehair (which is where the word "crinoline" comes from - it is literally this kind of material, and cage crinolines have been so called by way of comparison to real crinoline petticoats), which gave them a less-pronounced bell shape than the stereotypical hoop-skirted Victorian woman. Day dress was made with a pretty standardized construction: buttoning or hooking down the front to a point at the waist, with single/double/triple darts on either side (double darts did not become the absolute rule until the end of the decade), and a skirt made of squares or rectangular panels gauged to a waistband, most likely not attached to the bodice, perhaps made with tiered ruffles across it to help give the impression of a fuller spread. Fashionable sleeves were made to flare slightly from the dropped armscye down to the middle of the forearm or the wrist, and the empty space would be filled in with an undersleeve, one that was either a puff gathered to the wrist or a full ruffle. Evening dress differed in the bodice (which would fasten in the back, have short sleeves, and be open over the top of the shoulders and chest) and in the fabric, which would be lighter in color and weight. Hair would be parted down the middle and dressed low in the back, sometimes with hairpieces, producing a sense of mass. Bonnets were made with very little differentiation between the crown and brim, a form known as the "cottage bonnet", and would be close to a perfect circle around the face.

For outer wear, men would typically wear wool greatcoats over their ordinary coats. Women had a few choices. As you mention, shawls were very common - woven as squares with intricately decorated edges, corners, and centers, they would be folded in half and worn triangularly; the best were imported from India, but by this time there was a very robust European industry weaving them from fine wool. Short capes were another option, and there were even sleeved overgarments, although these were less common than one would assume. The cold was often being dealt with through people's everyday clothing - flannel undervests and petticoats, wool stockings, heavyweight fabric for gowns - and so outerwear did not need to be as entirely insulating as ours is today.

Feel free to ask any follow-up questions! I didn't talk about children's clothing, but I can if you're curious. I also have a Pinterest board of 1850s clothing, although Pinterest has sadly decided to delete all users' old notes/captions on pins, which is where I gave specific dates and museum accession numbers. You can also often find a lot of historic fashion plates at the NYPL's digital collection by searching "men/women/children [year]".