IMHO no, horses don't *generally* need conventional shoes & are *generally* better off without. **However, most domestic horses aren't managed in a way that allows their feet optimum health & function, so they do frequently need *protection* to accomplish what we want from them on any terrain.
This is one of those questions that you'll get polar opposite views on from different people, so it's important to do your own homework & educate yourself as best you can before making up your own mind. To that end, I started a thread for more info, which you'll find in my signature below.
~Do horses that ride on trails [packed dirt, fields, and roads] weekly need shoes?
No. For rough/hard ground they may require protection though.
~If a horse is housed somewhere with bedding on top and concrete underneath should it be shod?
Trouble with flat hard surfaces like concrete is the peripheral loading, especially if walls are overlong &/or the horse is shod in metal rims. Therefore they're better off bare & kept well maintained, or if they're spending a lot of time on paved ground, maybe boots with pads.
~Is there an alternative to shoeing?
There sure is. There are a wide variety of hoof boots these days, so you should find something suitable for almost all horses in most situations. Easycare have a huge range themselves. For what you're doing with your horses, sounds like boots are likely the best way to go. You only need to put them on when necessary & the horse is bare the rest of the time. So for eg. If you're going for your weekly trail ride, put them on for that, or if it's a big ride with only a small section of rough stuff you may even choose to carry the boots with you & just put them on for that section. The brand new Trail model have been getting great reviews for that kind of situation & they're about the easiest boot around to put on/off too.
Sorry if I am asking a dumb question. I am sort of a dumb person when it comes to shoes. :S
You're only dumb if you realise you don't know something & you don't ask!