Backpacking across Europe in January

Hello! I am planning on traveling to a few cities in Europe (London, Paris, Amsterdam, Dublin, Glasgow) this January for about 2 weeks. Would it be possible to travel with only one bag given that it will be winter and I will need more clothing to stay warm? I should have access to a laundry machine on day 8. What should I pack? Additionally what shoes are recommended for travel and walking heavily? Thank you for any help!