I’m unable to find vegan wool and I don’t like purchasing petroleum based products. What can I wear to keep warm?
Most vegan articles of clothing that do not rely on petroleum-based products are made of either cotton, hemp or linen. Since linen is often thought of as a summer-appropriate fabric, what you might want to do is use superposition (e.g. wear a linen shirt with a long-sleeved cotton T-shirt underneath). Hemp is a more versatile fabric with which you can make articles from underpants to denim jackets.
I knit my own sweaters. I either use recycled acrylic or organic cotton thread, but you said petroleum-based fabrics are off the table. Cotton is insulating when used correctly (you might want to turn to fitting articles of clothing for the closer to the body, the more efficient it is).
Bamboo is also known for being a great insulating fabric. Its producing can be very consuming in terms of soil and water though, so you might want to be careful to buy articles made from organic-grown bamboo.
This may not be a popular answer but everyone has to decide the ethics of this for themselves: Buy clothing from your resale shops. I still avoid anything with animal products from resale but, they have been produced already and the damage to the environment already done. By recycling it (through reuse, resale, or making their own as avazula suggested) I believe we: - atone for the waste and suffering already paid for during its production. - vote with one's money and resale or reuse does not vote for the polluting and suffering of new retail.
In summary Recycle and reuse whatever you can find in the resale shops, attics.
One of my favorite beanies was one I found laying out like trash on the street covered in dirt. I just dusted it off and washed it and it looks great, and won't make it into a landfill. Meets my vegan conscience.
You can make vegan cloths from plant fibers. You can use hemp and the flax plant for it. You can try to make it yourself, it is a lot of work though. I have seen linen being made from the flax plant, the fabric is a bit heavy. I'm not sure if it suitable for clothes though.
Both hemp and flax seed have seeds like you get with sunflowers as well. You can eat the seeds and even make cooking oil out of the seeds as well. It is a very versatile crop.
EDIT: well after doing some research it seems that ALL linen are made from the flax plant. I did not know that.