I have used a number of locally collected wood species in my aquariums, including cedar, without issue. The sample you show with the slime is too new based on the relative abundance and the appearance of the bark. The slime could be sap or could be a fungi growing under the bark.
If the wood is well aged then there will be fewer compounds that can leach into the water. One area I found that is good for collecting wood for aquariums is reservoirs. In the area along the banks is usually wood that has been cut down for the reservoir and the stumps and branches from this get aged by being repeatedly submerged then dried. Obviously you do not want to introduce any disease or parasites into the aquarium so you will want to clean the wood thoroughly before using. I boil or wash and treat with oxygen bleach. I then dry and clean the wood a second time before going into the aquarium. The cotton wood might be a bit soft for use in the aquarium but if kept submerged it might work ok. In a moist environment cottonwood will rot really fast, but it might last a lot longer if kept underwater. To me your sticks look ok but I am perhaps a bit reckless.
If you are going to use collected materials for your tank you will be taking a bit more risk of introducing something with negative consequences into your aquarium. I haven't had anything bad happen in my tanks but that could just be luck on my part. I would have no hesitation putting the wood
@madmark285 showed in his post into my tanks.
