We went to Amsterdam in the winter of 2013 because Fritz was giving a lecture at the university.
Amsterdam is very dog-friendly. Dogs are allowed in restaurants, cafes and most places. Although they should be on leash in shopping malls!
There aren't too many parks in central Amsterdam, but there are some wonderful parks in the Netherlands more generally. The Amsterdam Forest outside the city is great!
Just remember two tips:
1. Watch for bicycles when you cross the road!
2. Marijuana is bad for dogs, so don't take them into coffee shops.