I already posted “I agree with everyone else, the galoshes are a bad idea for hiking/backpacking.”
Now let me say this about wet feet. Your feet will get wet on the trail regardless of what you do. You see they will get wet either from the outside (rain, creek crossings, dew, etc) or from the inside (sweat). Now I don’t mind wet feet if I am in the tub or in the shower and the water and air temperature are warm. I do hate being out on the trail or outside anywhere with wet and cold feet. And you can get wet and cold feet on the high mountain trails in July and August (those mountain streams are really cold even in summer). It is not good to have wet and cold feet. That’s why I like insulated gortex boots and two pair of heavy socks----so even if your feet do get wet (from sweat–or from anything else), they will stay warm. The inner sock absorbs the sweat so your feet don’t ever feel wet, but when you take your boots and socks off, the inner socks are damp. Just hang them up and let them air dry. Or in winter, put the outer socks on first and the damp ones on the outside and let them air dry on your feet—if you hang them up in Winter, they will freeze and not dry.
Your feet will even sweat in tennis shoes. And your feet will sweat both in winter and in summer. Footware is a matter of preference, some like barefoot, some like real lightweight footware, some (like me) like heavy and substantial and gortex and insulated. It’s all up to you—how much do you want your shoes/boots to weigh and how much protection do you want on your feet/ankles? But wet feet you will get regardless—But do you want cold wet feet? I do not.
I have never had my boots get water in them during a pouring rain, but I wear 9 inch high boots laced snugly at the top, so the water can’t run down into them much. Also raingear keeps that from happening very much. Short boots could and I imagine would be more of a problem in heavy rain or extremely rainy weather----some of what many call boots hardly come above the ankle.
I hope this helps shed a little light on the subject of wet feet. TurkeyBacon is right about feet needing to breathe—they do. During breaks, it really helps if you take boots and socks off and let them and your feet air out—it feels so good. The heavy socks absorbing moisture (sweat) the way they do keep my feet feeling good even hiking in the hot summer----but taking boots off and airing out feet, boots and socks really does feel good and needs to happen especially when it’s hot. Also TurkeyBacon said “Footwear depends on your packweight to a large extent” and I agree as do the experts at REI (see their website). Heavy packweight, then you will need heavier more substantial shoes/boots and more protection/cushioning for your feet. Gaiters also like Papa Smurf said will help keep water out of your boots/shoes (and also rocks and dirt—and also help keep the poison ivy, briars, and ticks off of you somewhat).
So good posts by all, and I hope this helps and adds a little bit on the subject of wet feet. Keep on hiking.
Maintain