The City has had a long-time practice of giving away trees for planting to Seattle residents to help keep Seattle green. They have all now been spoken for EXCEPT now some were not claimed. Want a tree? The digging won't be that bad because the ground is so soaked. Info here. (Note: this is only for yard trees, not street trees, as you need an SDOT permit and that takes a week to get.)
Here's a great list of things to do during the holidays with kids but I pulled out the freebies.
Something fun for the kids: a free cookie decorating class, Tuesday, Dec. 21st.
Seattle Center is having their annual Winterfest with a plethora of fun and free stuff to do and see. They will be having ice sculpting this Saturday from noon- 2p.m. Celebrate the Winter Solstice, Dec. 22-23 at Seattle Center, 3:45 p.m. (With the actual Solstice being Tuesday the 21st at 3:38 p.m.).
Also, if you are downtown, the Seattle Sheraton's chefs build fantastic gingerbread houses you can view for free in their lobby at 1400 Sixth Avenue. Very pretty.
Not to be outdone, the Fairmont (411 University) has a Teddy Bear Suite (10 am-7 pm) and local school/youth choirs sing in the lobby weekdays from noon to 1 p.m. All free.
Or if you are by the waterfront, there are 50 LED-lighted toyland village displays at Waterfront Park (1301 Alaskan Way), also free.
And, there's a lunar eclipse on December 20th that will be visible from North America starting around 9:30 pm with total blockage at 12:16 a.m. on December 21st. Lunar eclipses are safe to the naked eye.