Perhaps someone will know more specifics about location. I am in Illinois so I don't know about your area. In general, beaches should be OK from the water up to dunes or vegitation. Be alert though to anything that might be animal habitat etc. Also, state parks, or national seashore areas are usually off limits. So, stay away from those. If in doubt, check with the local authorities or find a local Metal Detecting Club for recommended areas that are allowable to search and to see what restrictions they might have. Usually, I have noticed that they might limit times of day or year when crowds are down. They might restrict certain areas where there is native vegitation or wildlife habitat that needs protections. Bird Sanctuaries and dunes might be sensitive and they may not want digging there. Down in FLA where I go sometimes, there is a concern for Sea Turtles. They dig holes in the sand and burry their eggs. The areas where they do this are highly sensitive and very protected. Some of that stuff might be seasonal though and there may be certain times of year where there might be extra restrictions.
As for searching in the fall months, I don't know any Technical reasons you couldn't. As long as the weather is tolerable and the sand is loose enough to dig in, Around here, I would guess there will be a time where the ground will freeze and digging in the sand might even be a little rough. I don't know how your beaches get out where you are.
Also, there mgiht be some issues with cold temperatures and the display or readout on your detector. If you are using a detector like mine, (Whites XLT) that has an LCD display, cold weather can cause a slowing of the circuitry and the display. Batteries can also be deminished as it gets colder. Keep an extra set and keep them close to the body. Maybe carry a fanny pack with batteries and such under your coat to keep warm. The batteries in your detector might get week fast, due to the cold. You might just swap them for the warmer batteries and keep going. Then, as those batteries get cold, swap back. This time of year though, I don't know if the temps would be getting that cold that soon. Just got a call from a friend in MD last night. While we were around 50 here in Chicago, he was saying that he was still around 70 in MD.
Old coins should be findable anywhere where there is a history of people being there. You might have to listen harder for them though. Over time, objects, naturally, sink deeper and deeper. How deep is hard to say as it varies from type of ground to moisture conditions, wind..... Etc. Then there is the issue of restoration of shorelines. If a beach has been "Renourished" old items could be even deeper. Back to the beach I go in FLA, they renourished their beaches some years back. Some of the condos on the beach had their lawns, litterally up on the water line. At high tide, there was NO beach in front of them. One or two buildings had even lost their seawalls and one had lost part of their pool to erosion. I hadn't been down there in many years but last time I was there, I remember standing on a sidewalk taking pictures of the waves crashing over the rocks that had been placed to protect the seawall. Then, the next time I was there, they had more than 100 yards of beach in front of the buildings. Imagine the amount of sand that would have to be brought in to rebuild the beach. How deep anything that used to be there would now be after all that was dumped on top. Then again, a lot of the sand for the nurishment was dredged and pumped in from the nearby river channel and would be sand that had been washed away from the beaches in the first place. So, I wonder if it is possible that some of the good stuff could even be closer to the surface afterward, after being dredged and pumped back in.
Anyway, I would just say go out and have some fun. Don't get discouraged if you don't have a lot of luck right off. It can take some time to get a feel for detecting and understand your machine. The first few times I went out, I didn't find much. A couple pull tabs a penny or two, some foil. Now I find a good selection of stuff every time out. Swing in arcs from left to right and walk slowly. Covering a path about 2x your width as you go down the beach. Overlap your swings and don't swing too fast. Pay attention for any sounds that the detector makes. If you have a decent detector, and you search carefully and all, you will find stuff. I would suggest digging every good solid target. Compare what you are finding to the way it reads on any meters or displays. Compare your finds to how they sound or read out when you locate them. Then You will get a good feel for how your detector reacts to certain objects. What machine do you have. Does it discriminate? Does it have programs for hunting. Programs like Coin and Jewelry, Beach, Relic.... My machine has Coin and jewelry and Jewelry Beach. Jewelry beach is the same as Coin and jewelry but it has some specific tuning to compensate for effects of salt water. Being on Lake Michigan, (Fresh Water) I use the Coin and Jewelry about 90% of the time. I dig everything that is a good strong signal. I use headphones and listen for solid but faint signals and sometimes dig those as well. Even some broken signals can be good targets that are simply deep. I compare the sounds to what is reading on the meter. If it isn't IRON, I will usually dig it. On my machine, sometimes foil can be a nickel or a ring. A ring can often be a pull tab or a piece of foil... So, only rely on these readings as possibilities and not definites. If it is warm enough to tolerate, and there aren't many people around, which may be the case in fall, I know it is here, you might have an easier time getting out there and covering terratory. Use some common sense, Refill your holes and even off the sand after you are done. Make things look as nice when you are done as you found them. Take your trash or any that you find with you. I take a 5gal bucket with me and throw all my larger finds and trash in there. I then sort the trash from the good and pitch it. Avoid habitat and vegitation. Don't detect a state or national park area unless you have permission and made sure you understand the rules and restrictions that might be in place.