Always wear socks, whatever the type of boots, whatever the weather.
IMO, the most reasonably priced boots sold locally are those at Zara's.
But consider buying for the long term. You are likely to be travelling again. Boots arent' necessarily only for cold weather,more for comfort and safety. In NYC, you need so-called Winter boots -- the difference being it has a lot more traction, & lining for warmth/insulation. I do not think you need that for HK winter. Get something that will serve you well for at least 5 years. So, when you say "cheap"/reasonably-priced... do not think "throw away" or single-use, but your investment in comfort and style over x no. of years.