It is actually against the law to smoke an any federal, state, public or city parks in Oregon.
There is a smoke-free policy in Tigard parks (see https://www.tigard-or.gov/clean_air/). I have not seen signs posted about smoking (or not?) in Cook Park. The high school kids will come at lunch and discretely smoke off the trails and they are left alone. Generally true for the few I have seen smoking in the park. Just be respectful.
There is no rule preventing any from smoking there. Just use common sense no to offend anyone. If you don't mind me ranting for a second. I am not a smoker, but even I am shocked at the laws that are being made against smokers. Sometimes the dose law go too far and restricts the liberty of one group over another. Now the government has to hard on smokers. I understand the needs of nonsmokers, but come on 50ft from any building. No smoking in your own car. Too far.
Agreed with other answers, just try to keep the cancer to yourself if you must do it at a park where children are playing.
If you're responsible about it. Don't hand out cancer sticks to toddlers, and don't smoke while you're in the middle of a swarm of children. It's a common sense thing. Anyone that tells you that you're unable to is just being rude.
Yeah you can
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