It was a fun walk with our family (7 kids ages 8-18). They all enjoyed. Some were upset about all the mud they had to walk through, but after they all reconciled themselves to the fact that it was a trail of mud everyone had a great time. Yes at this time of year there was a lot of mud. At several points in the trail you had no choice but to walk in mud several inches deep. I think the best footwear is beach shoes, rubber boots, or sandals. Or if you have the feet for it just go barefoot.
We started from East Montlake Park and didn't go past the last island. For that area it was all flat, so no climbing hills.
Great hike for kids to check out the lake. Tons of birds and other animals. Renting a kayak or canoe is a great call here to see things from the other angles. You have to go to the other side of the lake (just to the north) to rent them but worth the trip. it can get pretty crowded here in the summer and on weekends.