I walked in the rain and found that there is a small cut on my toe, will i be at risk of some kind of infection?

Yes. : Any break in the skin puts the injured person at risk for infection because there is now an opening that can allow bacteria (or, rarely, fungi or parasites) to enter the body. The risk is higher the dirtier the foot was when it got cut (e.g. farmland with manure). Watch for redness and/or increasing pain, wash the wound once a day with soap and water and apply Bacitracin ointment and a bandaid.