I'm running for 25 minutes in 'cold' conditions -4 to 4C at the moment...
The climate is perhaps the most important factor to consider in buying your workout gear, so make sure to consider all possible weather conditions. You said the weather is cold, but is there rain or wind? Thick cotton sweatpants may keep you warm in cold weather, but in the rain you'll find its performance awful.
But what are other factors you should consider?
Like climate, the fit of trousers is incredibly important; after all, you don't want to be uncomfortable when running. If your clothing is too loose you'll constantly be pulling your pants up, and if it's too tight it is constricting and hard to run in. Since you cannot wear belts with running trousers, there are two typical ways to address this issue: elastic bands and drawstrings (and sometimes both). Ultimately this decision comes down to personal preference.
Additionally, you'll want to consider how breathable the fabric is. Many people like very breathable fabric while others might prefer to sweat when exercising.
Would buying them online be a good options or should you go to a running store to get some better advise?
Why not do both? You can go to a specialized store to try on various trousers and see which ones feel best, then you check them online to see if they're sold at a discount. Also, many online shopping sites (for instance, Zappos) have incredible return/exchange policies, so don't let the fear of choosing the wrong trouser be a barrier to ecommerce.