Sure. Missionaries always love mail. Just be aware that missionaries are trying to do their very best to work hard and stay focused. We are encouraged to uplift and positively influence them. The first several months of a mission are usually the most difficult due to being away from family and friends, dramatic change in lifestyle, homesickness, difficult working conditions, etc. So I would encourage you to help and support them by being positive and supportive. An idea might be to include an uplifting quote or story in your letter. 
 
But yes - anyone can write them. 
 
Good luck.