嗎 is used when there is no interrogative word or statement, taking place. Since 多冷 indicates "how cold", then there is no need to include 嗎. Note that 多 can be used to ask about capacity or measurement, even if it literally means "many".
No, literally 有多冷 is "to be how much cold" (有=to be when there's no subject with it) - or in this case "will be" because it's future tense. You might answer this with "it'll be very cold" but I think it's really asking for the temperature.