Padded gloves are a good idea. I rode and raced without gloves for decades (I always hated gloves and wanted to feel my bars). I ultimately developed severe carpal tunnel and cyclist’s palsy last year. It seemed to come on suddenly, and I woke up one morning with really bad parathesia (numbness, pins and needles) in one hand. Overnight, I was unable to button a shirt or tie shoes, and I could not grip or operate my bike brifters. I thought I had slept on my arm funny and it would go away. My doctors did a nerve study and told me I had a chronic nerve impairment from years of trauma to my hands and wrists. I ended up having carpal tunnel surgery that helped somewhat, but I still have some parathesia I live with and find myself dropping things frequently. I also have some stiffness in the joints of my fingers that likely are arthritic changes.
I won’t ride now — outside or indoors on a trainer — without gloves that have good amounts of padding over the ulnar and radial nerves. A trainer may actually be worse because you don’t move as much on the bike to relieve pressure on your arms and hands.
I wish I had used gloves earlier. My suggestions is to purchase a few pair, so you always have a set that are clean and dry to wear. After riding, mine come with me into the shower where I wash and rinse them out, and then are hung to dry.