If the snow has recently melted in Zurich but there's still snow on Uetliberg, you can sled on various locations along the Uetliberg range. I've described a few of the hills below. If you don't mind driving a little further, I can recommend Einsiedeln or Amden-Arvenbüel.
Uetliberg Schlittelweg (aka sled run)
With lots of snow, you can sled on a trail from the top of Uetliberg all the way down, 3.1km. I've never done it myself but I've heard it's fun, if a little scary. It's not always open, even if there's snow. Call the sledding hotline for info (0800 588 588) or visit their website. To reach the start point, take the S10 train to the Uetliberg stop. Walk up hill toward the lookout point and you'll pass the start of the Schlittelweg on your left.
Albis Pass sledding hill
For a normal sledding hill (walk up, sled down, repeat), drive or take a bus to Hinter-Albis, on Albisstrasse near Langau am Albis (5 mins south of Adliswil), about a 20 min drive from Zürich. There's a big parking lot and a big sledding hill. There are no services but it's free. On busy days, the landowner sells grilled sausages.
This winter trail isn't a sledding hill, but with lots of snow, you can pull the kids on the sled as you walk then sled down any parts of the trail that go down hill. Near the Felsenegg restaurant (about a 5 min walk from the Felsenegg cable car), there's a long stretch of an access "road" that people sled down (in below pic) and we've spent a fun hour there. The restaurant is cosy and has tasty traditional fare, but rather expensive.
The trail can be reached by the Felsenegg cable car in Adliswil (a short walk from the Adliswil train station) or by car to the Buchenegg pass near Langnau am Albis. This is a loop trail that starts along the ridge, then dips down through a couple farms before joining back up to ridge. For full details of this winter walk, see this post.
Do you have any local sledding spots you'd like to share?
View sledding with kids in a larger map