Yes, you can see the Rime ice trees from January to February. It won't melt from 7am to 10am. I think the late Jan is the best time to visit it and Jilin is just a good place to see the rime ice trees.
There is direct train from Jilin West Railway Station to Shenyang. You can find the specific schedule of China trains(https://www.travelchinaguide.com/china-trains/) on this website.
You can already see rime ice trees since early Jan. Yes, you need to be there in early morning. Will you just stay one day? Rime ice does not happen every day, so good luck to you.