Walking in the city centre

If the word has one syllable, you usually use the -er version of the word when making a comparison. "It was hotter..." "It was colder...", etc. If the word has more syllables, you use "more". "It was more temperate..", "It was more pleasant..." etc

In the past spring was "colder" here.

Italian doesn't have a large number of words to describe temperature; there is "freddo" and there is "caldo" and aside from perhaps "fresca" there isn't much in the middle unless you just add "abbastanza". However English has a larger range; hot, warm, cool, cold. I think in this case you may actually mean "cooler" rather than colder; spring in Rome generally isn't cold, though it may be cool.

I used to wear a pair of trousers, a t-shirt and warm shoes (sorry I don't know how you call in general the shoes that aren't like sandals).

1/ You would not normally use "trousers" to describe women's clothing. It would be understood, but it's not common. Most of the time "trousers" is used for menswear. "Pants" can be used to describe the clothes of either sex.

2/ It depends on the type of shoe, but "warm shoes" sounds fine to me. They would generally be enclosed shoes with flat heels; beyond that they can vary in design.

If I wear now these clothing like that now, I am too hot.

"Clothing" is a mass noun, so it's always singular; this clothing, not these clothing. (Though if you were referring to specific clothes you could say "these clothes".) In this case though I think you mean "clothing of this type", which can also be said as "clothing like this". (Though I have used "that" since this is closer to "quello" than "questo".) 2/ "Now" would have to be before the verb ("If I now wear..."; that would not be common) or at the end of the clause as I have shown.

A part Apart from that, I am glad that temperatures are increasing and the city now looks now more lively.

As I noted above, you could have put "now" after lively as an alternative.

Many tourists have arrived and they seem to enjoy the museums and the monuments. Sellers (especially the ones who sell ice cream and touristic tours) have become busier than usual, but everyone seems to work happily with the sunshine (or is it just my feeling?).

1/ "Sellers" is OK, but I would probably use "vendors" here. That's only because you use the word "sell" shortly after that and "Sellers who sell" sounds a little redundant. 2/ "Similarly 'touristic tours" sounds odd, and also redundant. You could just say "tours" or, if you want to emphasise the point that they are mostly for visitors to the city, use "visitor tours". 3/ "Everyone" is a collective noun and is therefore singular. You therefore need to use "Everyone seems to..." etc.

That was nicely written, though I should add that the last time I was in Roma the temperature was never lower than 30 degrees. Granite al limone save lives...

Walking in the city centre